Welcome to the forum, Nick!
I can empathize with with your situation. For any of us for which an interest in birding and in photography intersect, it is always stunning just how expensive quality telephoto glass actually costs!

Even now that I can afford L series glass, my natural thrifty inclinations cause me to be looking for the compromises between top quality and affordability.
Working on your questions in reverse: For close range, (50ft - home feeders etc) I started birding with a Rebel and a zoom topping out at 200mm and that worked fine for this type of range. However, you will soon find yourself needing even more reach and looking at the even more expensive, longer reach glass.

Unfortunately, that is a disease that we all suffer from and there is not cure as the manufacturers always coming up with better glass for more money.
I would say that the ideal compromise between cost and reach is at about the 400mm range. If I were in the US right now, I would offer you a lightly used Sigma 150-500mm Contempory lens, but I don't plan on being back until winter. (For a combination birthday/Father's day gift this year I went back to L series glass. Objectively, was it really worth the cost? Probably not, but I'm happy anyway. See, it never ends.) What I would say is that if you can't, or just won't, come up with more than the $500, you will probably have to look into used Sigma or Tamron.
A suggestion for finding whatever lens you decide you want; I have found that Craigslist is a possibility, but generally people want nearly new prices for lenses that you are taking a chance on. Hence, even though I had past success there, I gave up on it. Reputable dealers such as Adorama or B&H have used departments with lenses they have checked out and graded. I've had very good experiences buying both new and used with Adorama in particular. My current favorite is Tokai Camera in Tokyo, Japan, using their Amazon store. I've gotten excellent quality used equipment at very reasonable prices and with free shipping. This also has the advantage that being in Japan, most of their product tends to be the Japanese manufactured lenses. I see some possibilities in their extensive listings. Note: a little confusing at first, but after selecting a lens, you will have to click on the "see all buying options" button in the top right.
Amazon.com
One possible solution, that fits right into your price range is to consider switch over to a Canon Powershot SX-70. I have one as a backup and light weight carry around/travel camera. It is a mirrorless with a non-interchangable powered zoom of 21-1365mm equivalent. I paid $500 for mine a few years back and though not equivalent to my old 7D, it is a very reasonable compromise for the cost. It would have the advantage of being the same Canon menu, so easy to switch over from the Rebel.
Glad to help if you have any further questions.