You are opening quite a can of worms with this one! I have at least 3 rolls of 1961-d tilted/rotated rpm's that I can't identify.
When narrowing these down, I start by comparing the mint mark placement in relation to the date. This can "weed out" a ton of unlikely candidates very quickly. At this point I usually put a difficult coin in a plastic bag and label all of the possible rpm numbers it could be based on mint mark placement. Next, you can eliminate many possibilities based on the type of rpm it is (tilted, rotated, E,W,N, etc...). Hopefully, with a little work, you will be left with only one or two choices. Then you can begin to look for die markers, although with varying die states they may not be present.
When I look at your coin's mint mark placement in relation to the 1961D-1MM-077 they definitely don't match up (the -077's mm is much lower and centered). Therefore, you now know it can't be that one. It may take quite a while to compare all of the likely candidates shown on coppercoins to your example, but that's what works for me. Good luck!
Chugly