Results:
With limit: 27, 25, DNF = DNF
Without limit: 27, 25, 27 = 26.33
1. Scramble: R' U' F D2 U2 B2 D2 F U2 B R' B L' F2 L D B' L' B R U' F' R' U' F
Solution: U R D B' D' L2 F' B' L' D B U L U' L' B' R U R' U R U' R' U D2 B2 D2 (27)
U R D B' D' L2 F' B' //3x2x1 (8/8)
L' D //Pseudo F2L-1 (10/10)
(D2 B2 D2) //F2L-1 (pair ready) (3/13)
B U L U' L' B' //Random OLL to see what happens (6/19)
R U R' U R U' R' U //F2L + LL skip (8/27)
2. Scramble: R' U' F D' L2 D2 L2 U B2 U' B2 L' B D2 B' U F2 L' R2 U' B U F' R' U' F
Solution: R L U2 F' D' R B2 R' B' R B' R' B2 F' D' B' D F' U' B U R F2 R D2 (25)
R L //Partial EO (2/2)
(D2 R' F2 R') //Finish EO + lots of pairs (4/6)
U2 F' D' //3x2x1 (3/9)
(U' B' U) //Pseudo F2L-1 (3/12)
(F D' B D F) //F2L (5/17)
(B2 R B R' B R B2 R') //Sune (8/25)
3. Scramble: R' U' F U2 F2 L2 D' B2 F2 D' L R' D F' U' R' B' R2 F D U' B' R' U' F
Solution (only for no time limit): U2 F' U' B' D B D2 L D2 B L F L' F' B D L' D' U' L2 U L U' L U L' D' (27)
Premove: D' (found at the end to make lots of pairs)
U2 F' U' //Obvious 2x2x2 (3/3+1)
B' D B //Orient two edges (3/6+1)
D2 L D2 B2 //2x2x3 + 6 pairs (4/10+1)
Stop here if you want to have fun and try for yourself.
A possible continuation I've found:
B' //Save one pair (for F2L on R) (0/11)
L F L' F' //Insert other pair (4/15)
B D L' D' //Insert saved pair (4/19)
Antisune + AUF for 27 total
Another possible 27:
F' D F
L D' B' L B //All but a pair 3-cycle
L' F' L D L D' L' F //Pair 3-cycle
But I knew I was missing something really good. So I tried Cube Explorer and got this, which is very close to the first 27:
B' U' //Save one pair (for F2L on R) (1/12)
L F L' F' //Insert other pair (4/16)
L U L B //Finish (4/20)
I was frustrated for DNFing #3 and not finding a good solution even without time limit. Cube explorer ending to my start is very nice though.