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Well this is here now so to answer your question
there is no one method you should use for FMC except maybe DR my advice is learn eo, blockbuilding, niss and insertions which jperm and speedcubereview have good tutorials on and if you want to get really good learn DR
if you don’t want to learn fmc techniques I would still advise against corners first methods as they tend to contain lots of slice moves which are generally bad for fmc as they are counted as 2 moves

Well this is here now so to answer your question
there is no one method you should use for FMC except maybe DR my advice is learn eo, blockbuilding, niss and insertions which jperm and speedcubereview have good tutorials on and if you want to get really good learn DR
if you don’t want to learn fmc techniques I would still advise against corners first methods as they tend to contain lots of slice moves which are generally bad for fmc as they are counted as 2 moves

A mediocre? terrible? first attempt at DR. Went well over an hour too. :/

Scramble: F L2 B' D2 R2 F D2 B' L2 U2 B' D' U B' R' F U F' L D' B2
(U R2 D' L D') // belt (5/5)
(L2 F B' D' F' B') // EO (6/11)
(R @ D L' D' L2 D L' D') // CO (8/19)
(U2 L' U2 R B2 D2 R F2 L' F2 L2) // corners; ab2e2e (11/30)
@ = (R B2 D2 B2 D2 B2 D2 R') // 2e2e (8−1/37)
Solution (37): L2 F2 L F2 R' D2 B2 R' U2 L U2 D L D' L2 D L D' R D2 B2 D2 B2 D2 B2 R2 B F D B F' L2 D L' D R2 U'

A mediocre? terrible? first attempt at DR. Went well over an hour too. :/

Scramble: F L2 B' D2 R2 F D2 B' L2 U2 B' D' U B' R' F U F' L D' B2
(U R2 D' L D') // belt (5/5)
(L2 F B' D' F' B') // EO (6/11)
(R D L' D' L2 D L' D') // CO (8/19)
(U2 L' U2 R B2 [email protected] D2 R F2 L' F2 L2) // corners; ab2e2e (11/30)

You can insert your 2e2e in a different spot to get a 6-4 (!!!) giving 32 final!

@= (B2 D2 B2 D2 B2 D2) // 2e2e (6-4/32)
Solution (32): L2 F2 L F2 R' B2 D2 B2 D2 R' U2 L U2 D L D' L2 D L D' R' F B D F' B L2 D L' D R2 U'

Getting a 2e2e insertion this lucky is incredibly rare, by the way. I'm wondering, how you didn't see this?? Did you not check your whole skeleton or something? You missed out on this awesomeness.

That is a pretty good first DR attempt overall! I'm glad you know that working on solving the corners after DR is a good thing to do. Keep that up ^^

As for getting to DR, you did it in a pretty interesting way. Lol. Cool.
Generally, people get to DR by doing this:
EO -> Reduce to 4c4e, 4c2e, or 3c2e (the number of corners and edges that are not DR'ed / misoriented) -> Set up to the trigger using domino moveset -> Apply one of these short triggers, R, R U2 R', or R U* R' respectively, and now you have DR in about 12 moves (instead of 19).
Here is a good resource for DR- https://drive.google.com/file/d/1DSvekOdhadXyZg60-0felZIMELfTs_XP/view?usp=sharing

Also, there is a Fewest Moves Facebook group that you can post cool solutions or ask for help and advice or participate in challenges and it's a pretty active community, unlike here on speedsolving.com. I invite you come take a look, and good job on venturing into DR territory for the first time!

Trying to do FMC at 4 am probably explains a lot. I actually did the 2e2e first, which led to a standard last slot + T perm finish, then I guess I tunnel-visioned when I removed the 2e2e and tried to insert it somewhere else.

I'm pretty bad at EO starts in general and I didn't really manage to find anything useful starting with EO. (Yet? Still working on it!)

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edit:

Same scramble, but with a more sensible 13 DR now. Really struggled with trying to figure out how to set up the 4c2e; the domino solve was just blockbuilding (instead of corners first because I couldn't figure out how to do that without too many moves).

(U R) F L' // EO (4/4)
U B // to 4c2e (2/6)
(U B2 L2 R2 U2 D F) // DR (7/13)
F2 D' R2 D' U L2 U2 F2 U F2 L2 // ab2c2e (11/24)
Skeleton: F L' U B F2 D' R2 U D' L2 U2 F2 U F2 L2 F' D' U2 @ L2 R2 B2 U' R' U'
@ = D R D' L D2 R' D R D2 R' L' // J perm (11−4/31)
Solution (31): F L' U B F2 D' R2 U D' L2 U2 F2 U F2 L2 F' U2 R D' L D2 R' D R D2 L R B2 U' R' U'