There are plenty of options around here but none of them, unfortunately, exactly fit your criteria. Outside of A-class you are not likely to see $2,000+ rent for a 3-bedroom and if you do, the price is going to be way higher than the range you mentioned. Anecdotally I can tell you I bought a 3/2 in downtown Raleigh for $320,000 off market (no agents, so almost as 10% discount to market) that is renting for $2,200/month and that is even a little rich for the area (East Raleigh). There are some interesting pockets in the "dells" Wendell, Knightdale, Shotwell, etc. where you can likely find something in the 200k range that will rent for $1,400-$1,500 which is going to get you to about a 0.75% rule versus something closer to 2/3% in the immediate municipalities in the metropolitan statistical area (MSA).
I also want to add some caution as far as overall pricing is concerned. The national market has seen excessive rebounds beyond comprehension (roughly 10% y/y), and they are even higher on a percentage basis in our region (roughly 15% y/y). Those are not the most accurate or best statistics but generally representative. At the same time we have sales exceeding starts so as already mentioned in here the inventory is very thin. My biggest concern is the February rise in interest rates. According to Morgan Stanley's equities team (Thoughts on the Market, a great podcast), the initial jump in rates is not of major concern; however, 8 out of 8 of the last rate bottoms have resulted in market corrections approximately 12 months out (spring 2022 at this rate). At the same time we have elevated equity relative to the last housing crisis and lower ownership rates, meaning there should be plenty of buying potential. While these points all seem somewhat scattered and unrelated they actually illustrate the uncertainty and what may be categorized as panic buying.
Personally, I think there is a strong chance of a correction or at least abrupt stabilization in the 2022 spring market, but prices should continue to increase at least until that time and possibly beyond. The good news is that rents in the Raleigh area are still unquestionably lagging and have ample room for growth to catch up to prices. If you are buying and holding you can withstand negative price shocks because the rent will still come in at the same rate and your equity position is somewhat irrelevant (depending on your financing strategy, likely).
We are personally shopping for similar deals, but not overpaying and beginning to hoard a bit more cash in the event of any sort of a correction.