This is how RoboManus jumps
Language: asm
loc_0_CF21:
$CF21:20 4A CF JSR sub_0_CF4A A:00 X:04 Y:00 S:FB P:nvUBdIZC
sub_0_CF4A:
$CF4A:FE DF 03 INC Obj_various_cnt,X @ $03E3 = #$4F A:00 X:04 Y:00 S:F9 P:nvUBdIZC
$CF4D:BD 83 05 LDA objects_some_anim,X @ $0587 = #$84 A:00 X:04 Y:00 S:F9 P:nvUBdIzC
$CF50:49 F0 EOR #$F0 A:84 X:04 Y:00 S:F9 P:NvUBdIzC
$CF52:4A LSR A:74 X:04 Y:00 S:F9 P:nvUBdIzC
$CF53:69 10 ADC #$10 A:3A X:04 Y:00 S:F9 P:nvUBdIzc
$CF55:DD DF 03 CMP Obj_various_cnt,X @ $03E3 = #$50 A:4A X:04 Y:00 S:F9 P:nvUBdIzc
$CF58:60 RTS (from sub_0_CF4A) ---------------------- A:4A X:04 Y:00 S:F9 P:NvUBdIzc
$CF24:B0 1E BCS loc_0_CF44 A:4A X:04 Y:00 S:FB P:NvUBdIzc
$CF26:A9 00 LDA #$00 A:4A X:04 Y:00 S:FB P:NvUBdIzc
$CF28:9D DF 03 STA Obj_various_cnt,X @ $03E3 = #$50 A:00 X:04 Y:00 S:FB P:nvUBdIZc
$CF2B:A5 26 LDA RandomValue_2 = #$15 A:00 X:04 Y:00 S:FB P:nvUBdIZc
$CF2D:29 02 AND #$02 A:15 X:04 Y:00 S:FB P:nvUBdIzc
$CF2F:09 05 ORA #$05 A:00 X:04 Y:00 S:FB P:nvUBdIZc
$CF31:9D C0 04 STA Objects_Z_speed,X @ $04C4 = #$FE A:05 X:04 Y:00 S:FB P:nvUBdIzc
$CF34:A5 27 LDA RandomValue_3 = #$89 A:05 X:04 Y:00 S:FB P:nvUBdIzc
$CF36:29 80 AND #$80 A:89 X:04 Y:00 S:FB P:NvUBdIzc
$CF38:9D 56 05 STA Objects_dir,X @ $055A = #$00 A:80 X:04 Y:00 S:FB P:NvUBdIzc
$CF3B:BD 83 05 LDA objects_some_anim,X @ $0587 = #$84 A:80 X:04 Y:00 S:FB P:NvUBdIzc
$CF3E:9D 65 05 STA Objects_X_speed,X @ $0569 = #$00 A:84 X:04 Y:00 S:FB P:NvUBdIzc
objects_some_anim increments by $C every time you hit him, and Obj_various_cnt increments until it overcomes the messed up value of objects_some_anim (SHIFT(XOR(a, 0xf0), 1) + 0x10), then a jump happens and Obj_various_cnt resets. The speed and direction are random, but you can't get vertical speed other than 5 or 7.
tl;dr: doesn't look manipulatable.
EDIT:
After RoboManus we're
02:30.37 ahead.