To Gut or not to Gut? House Remodel?

One possible solution to stay within budget is to remodel one room at a time. Take it down to studs, run new mechanicals, insulate, drywall, paint, trim, and then go on to the next area. You can probably advertise for tradesman who would be willing to do what you need done on the side, which will save you money. You will get a huge return on investment with the insulation, and your home will be brought up to code. Hope this helps.