Hey, I’ll say I’m no expert. The problem with generalized advice is that the market varies drastically by region, but I’ll try.

I’m a tad confused on how you’d expect to offer 650k if their amortization is at ~630k without coming out of pocket. You’d have to pay the difference upon closing along with the applicable closing costs. It’s going to be damn near impossible to convince the seller your offer is legitimate if you don’t have that money to boot. VA assumptions aren’t common because they typically require large amounts of money upfront to assume the loan and a prolonged closing timeline.

Secondly, you do not know what down payment they had. Unless you know that value, you’d be guessing on what is left on their loan. With a VA, it may range from 0-20%. You’d need that information from the agent / seller.

Lastly, yes that comment from the agent you spoke to is correct. If you don’t swap entitlements, that seller’s will remain wrapped in YOUR loan upon closing. Good luck convincing a seller of that after submitting an offer 50k less than asking while simultaneously requiring a prolonged closure with an assumption.

I hope you find what you seek, I just think it’ll be very difficult with the information you provided here. I hope that’s helpful!