I've discussed with a few others and only one does programs like these - essentially they have no info on what options I might have besides a conventional loan with 3-20% down.

But if you've got 20% to put down conventionally you should be able to find $100 a month all day long.

They offer a 2-year residential bridge loan for this purpose (bridging the gap between hard money or c/c debt, and a long term refi).Granted, you'll pay a couple of points and higher interest rates than conventional, but you can also buy yourself two years, pay off your credit card debt, and set yourself up for a conventional refi at a very low interest rate in a few months by cleaning up your credit score.

Is it possible for me to find a conventional loan with these terms?

(Savings, Hard Money, Conventional Loan, etc.)What was the worst part of the process?

If you go with a relatively turnkey strategy then you just need a traditional lender to get a conventional or FHA loan (or VA if you are a veteran).

Only downside is the interest rate may be higher than a conventional mortgage (I was getting quotes of 3.99%, 30 year, amort. with 25% down). 

First-time buyer here, and have a preapproval for conventional 3% down.

You'll likely have a little better luck going FHA as it is a little more lenient on the employment history than Conventional.

Conventional financing 5% down no PMI first time home buyer program.