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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'

The scramble has 4 bad edges on F/B but they are in a pretty bad spot.
(F') - (which is F' on the inverse scramble) orients 2 edges + misorients 2 edges leaving 4 bad edges (but in a different spot)
When switching back to the normal scramble, all 4 bad edges are on the F face, F' orients them.

Remember that (F') F' is obviously not the same as F' F' and therefore not F2 (which wouldn't orient any edge btw)

The scramble has 4 bad edges on F/B but they are in a pretty bad spot.
(F') - (which is F' on the inverse scramble) orients 2 edges + misorients 2 edges leaving 4 bad edges (but in a different spot)
When switching back to the normal scramble, all 4 bad edges are on the F face, F' orients them.

Remember that (F') F' is obviously not the same as F' F' and therefore not F2 (which wouldn't orient any edge btw)

I didn't do badly in FMC for once and got 6th at Cubing at Home 1.2 on Saturday

Spoiler: Background Story

Ok so the last proper FMC attempt I did was in late April/early May (calendar week 18) and I've been struggling with FMC since March so I didn't expect to much going into this. Additionally there were less than 3 hours left when I realized that FMC was going on.
Because I mainly focused on finishing the attempts in time (I had 50mins left for the 3rd attempt) I pretty much felt no pressure after the 25 and 26. My PB Mo3 was 28.67 so I basically only had to not DNF the 3rd attempt. Luckily the 3rd attempt was a pretty good one too so I got a 26.00 PB Mo3!
Only the 2 World Champions, the WR holder, James and AJ beat me so that was pretty epic.

Spoiler: 26.00 Mo3

Spoiler: 25

R' U' F U' R2 U' L2 U2 F2 R2 F2 L D2 B' L B' D2 R B D R' D R' U' F

L2 B U2 L // EO
D2 F2 L2 U2 D’ B’ // DR
L2 B2 // 222
(D2 R2 D2 F2) // 223
(R2 D’) // AB3C

L2 B U2 L D2 F2 L2 U2 * D’ B' L2 B2 D R2 F2 D2 R2 D2
* U B2 U’ F2 U B2 U’ F2

L2 B U2 L D2 F2 L2 U’ B2 U’ F2 U B2 U’ F2 D’ B' L2 B2 D R2 F2 D2 R2 D2

Spoiler: 26

R’ U’ F L’ D F2 U2 F’ D B U2 R2 D2 L2 U2 L F2 R2 L B’ L F R’ U’ F

D L (U B’ L) // EO
(D2 L2 B2) // p222
(U F U’) // p223
D F’ D’ F U2 // pF2L-1
F D2 F’ D U // AB3C

D L D F’ D’ F U2 * F D2 F’ D U2 F’ U’ B2 L2 D2 L’ B U’
* R’ B R F R’ B’ R F’

D L D F’ D’ F U2 R’ B R F R’ B’ R D2 F’ D U2 F’ U’ B2 L2 D2 L’ B U’

Spoiler: 27

R' U' F L2 U F2 B R B R' F D2 L2 F' R2 F' R2 D2 B2 D B2 U R' U' F

D’ F U’ B // EO
(R U’ R) // 123
U’ L’ U2 (U’) // 223
R’ D’ R’ // F2L-1
D2 F D’ F’ D2 F D’ F’ D’ // AB3C

D’ F U’ B U’ L’ U2 R’ D’ R’ D2 F * D’ F’ D2 F D’ F’ D’ U R’ U R’
* F’ D B D’ F D B’ D’

D’ F U’ B U’ L’ U2 R’ D’ R’ D’ B D’ F D B’ D2 F’ D2 F D’ F’ D’ U R’ U R’