Alright, taking it from the top:
It looks like you're trying to do the right things. I don't think that you're in an unmanageable situation, so we should be able to work you through it.
Now that you've got the foam out, at least you can identify where the leaks are occurring. Start with a dry boat on the trailer, and then fill it slowly. Mark any leaks you find on the underside with a marker. If the leaks are coming from the rivets, you can either try to re-buck the rivet (will need some help) or remove it and re-rivet with a closed ended rivet. If there are cracks in the aluminum around the rivets, depending on the size, you may need the help of a welder. Others here have more experience fixing leaks, I didn't have to deal with much at all on my re-build.
The poured in foam does provide some support, but it's not as much as you might think. Take a look at this build, he's done about the same thing that you're doing: https://www.tinboats.net/forum/viewtopic ... 21&t=17704
I have the Pro-17, which has a different rear deck than yours. On mine, there are two or three aluminum L-brackets that run across the area where the foam is. These provide most of the structure. You shouldn't have any problem using sheets of closed cell foam from HD or Lowes. I would stand them on end, and stack them side by side. If you're concerned about structure, you can custom cut each piece to make a perfect fit between the bottom of the hull and the underside of your decking. You should gain back all of the strength, if not more than the original poured in foam. I tend to try to stay away from the pool noodles, as they have a habit of absorbing water over time similar to the original foam you had. Think about a noodle that's been in the water for one or two years, and you can see what I mean.
I would definitely replace the foam. It will keep your boat from sinking completely if you ever hit something or if your bilge pump begins to fail. It doesn't take much in the way of a few good waves to swamp the back of a bass boat, being so close to the water. Once you have one or two good waves go over, there's nothing you can do about it. With out foam, you have nothing but what's on your body to help you. With the right amount of foam, at least you have a life raft left, and you can pull the whole thing back to dry land.
Keep posting questions and progress, and I'm sure that you will be able to work through any issues.