Since they are on a crunched schedule (they have to move out of state at the beginning of May), can we push to make them pay for all of this? I mean, they have to get these fixed if they want to sell the house to anyone else right?
You need to consider what you're asking them to do.
1. "Push to make them pay for all of this": they'll hire the cheapest contractor they can find to make it look as good as possible. It won't be done with quality materials, and it won't be done by craftsmen who care.
2. "Reduce the price of the house": You have to come up with an estimate of how much you want the price to be reduced. Part of that is the cost of the repairs, part of it is compensation for your assumption of the inconvenience. Then you have to hope that your repairs actually come in under your self-imposed "budget".
3. "Negotiate the repairs": Usually done by getting several estimates, you get to choose the contractor, they get to pay some average of the estimates. That way everyone's equally less than happy. Again it puts a lot of pressure on the contractor to finish the work before the seller moves, so you may not get a quality job.
4. The seller's other option is to wait for either a) a foolish buyer who won't do their diligence like you're doing, or b) a buyer who knows exactly how they want to tackle those repairs and will cut a deal more quickly than you will. Of course you got there first, so your offer has priority until someone figures out a way to wiggle out of the deal.
Despite all the scary words about carbon monoxide and gas-fueled fireballs, mechanically the repairs are fairly straightforward. I wouldn't personally tackle the rotting beams because it's a job for a contractor with experience & quality tools, but I suspect that you'll find the beam rot was caused by the standing water under the house. If there's a bathroom near any of the rot then you should do an additional inspection there for leaky pipes or leaky drains, but the repair itself sounds like it'll be under $10K.
When your inspector delivers his report, you could ask him and the realtor for referrals to contractors to handle the repairs. You should accompany the contractors as they make their inspections (so that you'll understand the job scope and learn about their work quality) and get written repair estimates. Then you should ask the seller to reduce the price by the amount of your estimates. You want to handle the repairs on your own time and your own schedule, when nobody has any pressure to finish the job too quickly.
Your instincts are correct: falling in love with real estate is foolish because it almost never reciprocates. If you're not happy with your choices then just walk away from the deal. You either exercise one of the contract's contingencies or consider it $1000 tuition at the Real Estate School of Experience.