I’m kinda a newbie myself- nonetheless, I have opinions.
1) Used ebikes are not a significant option for 2 main reasons: one, the field is changing very quickly and two, used ebike means used battery. You probably want to know how much life is left in this (very expensive) part of your bike.
2) You’re in luck, because there are many stores selling and supporting ebikes in Austin. I’ve rented ebikes for a very reasonable price at the Bicycle Sport Shop on S. Lamar at Barton Springs Road. Riding a few bikes is really a great way to figure out what you want.
3) Others will point out how wrong I am in this last point: I think a quality experience will cost you more than you’ve budgeted. There are many attractive options from reputable companies that will come with 2 years of dealer support- for around $3K. Right now there are some models from last year (particularly from Haibike & Stromer) that you can get around $2K.
4) If you pay Austin utilities you’re doubly in luck, because there is a rebate in place for ebikes- up to $300 for bikes above (I think) $2K.
Good luck!