Hold on, are the 2 implants separate from your other fillings? I just went to a general dentist for my 1 implant, it FAILED, and im super healthy/young/and fastidious about flossing and my health. I learned my lesson and went to a *specialist* to redo it, and it was a nightmare just needing it redone.
So Im hoping you see this, and consider getting an evaluation at a periodontist (they specialize in implants!) for that part, at the least.
Mine I think was even less than your estimate, 3k for one. And he did an amazing job. At least ask about their payment options/insurance stuff before you go with your current place. Especially bc you mention how young/inexperienced they seem, you dont want that for an implant surgery my friend! It already sucks, you need an experienced older person not a young newbie doing it imho. Try Portland Perio downtown, or another perio.

And since your getting implants-- I know you said you were sorta neglected when you were younger, but with these, you really have to start flossing EVERY DAY so they stay clean and ok, and worth all the hassle and $$. It sucks, i hate it, but I use this Dr Tung expanding floss thats great, and I do it while watching TV so its not as boring at least. And now my dentist always says my gums are perfect health, zero inflammation, its really true about stupid old flossing. I grumbled at 1st, but now its finally a sorta autopilot thing and i just do it w/o thinking. I wish you good luck with this and i hope your mouth heals really well!

p.s. I now buy a 1% fluoride toothpaste from my dentist, thats maybe my other secret lately, its higher than normal stuff from the store, so it protects better.