Interesting theory you have there. If you would allow me a few thoughts?
Who drags themselves five miles or more to a river, while perishing of bloodloss, then wanders around in the woods for at least six hours gathering paint supplies, then mixes the paint, and then decorates themselves in such detail? There is 0% chance of staying lucid that long with such grievous injuries.
Not to mention that it had been days, maybe a week, between the tracker jackers and when Peeta logically would have obtained the wound. [til she finds him]
To me it seems logical he would try to get to water if he were, and he was, in such bad shape. You'll die sooner without water than you will food, and any food you might be looking to catch has to come get a drink sometime too. So it's a good place to be. I'd like to know where you come up with that it was 5+ miles to the stream, was it a guesstimate? Was it shown that it seemed to be that far in the movie, because I've not seen that?. In the book it doesn't say, and from Katniss' point of view after her stings work through her system, it wasn't that far til she found the stream which she would later follow back toward the Career's camp and wind up finding Peeta, so I don't think it was as far as all that, maybe a mile, two - two and a half tops.
What we do know is he was cut immediately, and that it was Cato who did it, and that he meant to kill, because at the victor's wrap up Katniss sees how he fought Cato to ensure her escape from the scene. And Cato was boasting about it at the lake when Katniss goes to blow up the supplies. So he was cut the day of the attack, and here, I agree with you on the oddity of his surviving between the Tracker Jacker attack and the blood loss because it does take Katniss nearly a full week to find him. (She was out 2 nights with the stinger venom, she spent the one night with Rue, she spent a night by the camp after blowing the supplies and then she spent two nights mourning Rue, the night of her death and the next night, which was also when the rule change announcement was made. So she located Peeta on the stream mid-morning or so of the 7th day.) He should have died of dehydration before then. Unless you postulate that he was not in the dire straights she found him in until a few days later. Cato's "sure cut" failed to kill the tribute from District 8 on the first night, and with added difficulty of attacking while under the influence of the Tracker Jacker's venom, he once again seems to have missed anything vital. It states the wound goes down to the bone, but unless you hit an artery, that's survivable. It's the infection and how weak he is that is killing him when Katniss finds him, not the wound itself. So if he held out a few days, and he would have had to simply because as you state he would not have been lucid enough to manage it for at least a day and a half after the Tracker Jackers during which time the Careers wouldn't have been able to track him either, but if he held out for a couple days beyond that before having to bury himself, he would be in okay shape water wise by the stream. Also, Katniss' flight under the effects of the venom seems to indicate that he could have covered the distance to the stream, wounded as he was on some kind of adrenaline high, and he too was running for his life, so it wouldn't have been as hard to make it to cover the distance to the stream as it might have been, had he simply been wounded, without the venom, and without the fleeing for his life.
I don't think it would have taken that long to gather camouflage supplies by the river either, he used the mud and vegetation that was already there to do the trick. No mixing, no real "gathering". Plus if as we've presumed above, if he made it a few days before having to hunker down and accept dying in the mud, he would have had time to gather anything he would have needed to. Still, I doubt he would have needed to spend that much time gathering things even if he had to do so immediately. Once again I'm wondering if it was implied he spent time gathering supplies in the movie? Because I don't see that mentioned in the book, in fact it doesn't seem to mention anything at all about Peeta from the time of the Tracker Jackers, to when Katniss finds him, she tells about herself, and he talks about when he first started having a crush on her, but she never asks what went on between the attack and fight with Cato and her finding him on the stream bank. So we really can't know how long he was up before he had to bury himself and hide.
And while he supposedly allied with the Careers only for the purpose of steering them away from Katniss, and protecting her, he consistently led them straight to her campsites.
Again, are you inferring that he led them to her from the movie? Or just because he happened to be with them and they ran across her a couple times? Both times we see them run across her in the book are perfectly natural, Not because Peeta, or even the Career's, were specifically tracking her, though from the sound of it, they were, and Peeta would have just been along to protect her should the need arise.
The first night they followed the beacon of the campfire the girl tribute from District 8 lit to keep warm. (the one Cato failed to kill with his "sure cut") Neither the Careers nor Peeta even knew Katniss was near by. The second and last time they find her while Peeta is with them was the fourth night out, and was because that day's fire, the one sent by the Gamemakers, had driven them all together, and Katniss, fleeing for her life as she was and with her injuries, wasn't as careful about not leaving a trail as she would have been otherwise. Then she also proceeded to sit out in the open by the pond for quite a while.
The only possible explanation for the river incident is that he painted himself, cut his hand to leave the prints beside the river, and then asked Cato to slash him- or slashed himself. Meaning that he was a Career all along, and had set up a trap to lure Katniss in so his posse could pounce on her while she tended Peeta's wounds.
As touched on above, we know Peeta was cut the day of the Tracker Jacker attack by Cato because he was helping Katniss escape. We also know that if he were a Career, he would have simply killed her himself when he found she had come back to the Tracker Jacker scene to retrieve the bow and arrows from Glimmer's body, instead he told her to run. Then as we hear during the victor's wrap up in the Capital, he actually fought Cato to ensure her escape.
That it was a trap to lure Katniss in would not have been a good strategy for Peeta or the Careers to consider either, since they would have no guarantee she would come find him until after the rule change on the sixth night after the attack. And by that time Peeta was too weak, and his leg far to infected to have put the strategy together and enacted it the night before. Plus we already know when and why the wound was inflicted, and that Peeta was misleading the Careers and actually fighting Cato off to help Katniss.
I agree with you, with the time line given, he probably should have died of dehydration before she found him, or from infection. But I don't think the plot-hole is nearly as big as you followed your "what-ifs" into. :)