Looks pretty awesome! I like the title screen, and how well the modified graphics blend together (to me).
Concerning the turnips, I tried to look into it for you.
0x1CDF - 96 - Turnip (Top tile)
0x1CE0 - 97 - Turnip (Bottom tile)
0x1FAC - 02 - Turnip Palette Attribute (Top, Green)
0x1FAF - 01 - Turnip Palette Attribute (Bottom, Red)
If you want both tiles of the turnip to use the green palette, change 0x1FAF to 02.
If you want both tiles of the turnip to use the red palette, change 0x1FAC to 01.
Similarly, you can change both to 00 or 03 to use the other parts of the sprite palette.
That way, both tiles will use the same part of the palette, since that seems to be what you would prefer, by the sounds of it.
As for being able to use 4 tiles for the turnip instead of 2, that might require some work. Unfortunately, that might be beyond me.
Here are some pages you might want to read concerning sprites:
PPU OAM - Nesdev wikiPPU sprite evaluation - Nesdev wikiSprite size - Nesdev wikiMost programs write to a copy of OAM somewhere in CPU addressable RAM (often $0200-$02FF) and then copy it to OAM each frame using the OAMDMA ($4014) register.
Here is $0200-$02FF (0x100) in RAM when the emulation is paused as soon as Phase 01 appears on the screen.
2D FF 20 88 - Weird sprite, X: 88, Y: 2D, palette 0, unimplemented
90 6A 42 79 - Top of smick's back, X: 79, Y: 90, palette 2, horizontal flip
98 6B 42 79 - Bottom of smick's back, X: 79, Y: 98, palette 2, horizontal flip
90 68 42 80 - Top of smick's front, X: 80, Y: 90, palette 2, horizontal flip
98 69 42 80 - Bottom of smick's front, X: 80, Y: 98, palette 2, horizontal flip
50 6A 42 E9 - Top of smick's back, X: E9, Y: 50, palette 2, horizontal flip
58 6B 42 E9 - Bottom of smick's back, X: E9, Y: 58, palette 2, horizontal flip
50 68 42 F0 - Top of smick's front, X: F0, Y: 50, palette 2, horizontal flip
58 69 42 F0 - Bottom of smick's front, X: F0, Y: 58, palette 2, horizontal flip
EC FD 42 F1 - Blank sprite
F4 FD 42 F1 - Blank sprite
EC FD 42 F8 - Blank sprite
F4 FD 42 F8 - Blank sprite
EC FD 42 F1 - Blank sprite
F4 FD 42 F1 - Blank sprite
EC FD 42 F8 - Blank sprite
F4 FD 42 F8 - Blank sprite
51 96 02 6C - Turnip top, X: 6C, Y: 51, palette 2
59 97 01 6C - Turnip bottom, X: 6C, Y: 59, palette 1
61 96 02 BC - Turnip top, X: BC, Y: 61, palette 2
69 97 01 BC - Turnip bottom, X: BC, Y: 69, palette 1
ED FD 02 F4 - Blank sprite
F5 FD 01 F4 - Blank sprite
3A 00 00 18 - Professor (left side, front, head), X: 18, Y: 3A, palette 0
42 01 00 18 - Professor (left side, front, hand), X: 18, Y: 42, palette 0
4A 02 00 18 - Professor (left side, front, foot), X: 18, Y: 4A, palette 0
3A 03 00 20 - Professor (right side, back, head), X: 20, Y: 3A, palette 0
42 04 00 20 - Professor (right side, back, hand), X: 20, Y: 42, palette 0
4A 05 00 20 - Professor (right side, back, foot), X: 20, Y: 4A, palette 0
F4 00 00 00 - Doesn't appear: Professor sprite, X: 00, Y: F4, palette 0
F4 00 00 00 - Doesn't appear: Professor sprite, X: 00, Y: F4, palette 0
F4 00 00 00 - Doesn't appear: Professor sprite, X: 00, Y: F4, palette 0
F4 00 00 00 - Doesn't appear: Professor sprite, X: 00, Y: F4, palette 0
F4 00 00 00 - Doesn't appear: Professor sprite, X: 00, Y: F4, palette 0
A8 54 01 1C - Dynamite fuse, X: 1C, Y: A8, palette 1
B0 50 03 18 - Dynamite, X: 18, Y: B0, palette 3
B8 51 03 18 - Dynamite, X: 18, Y: B8, palette 3
B0 52 03 20 - Dynamite, X: 20, Y: B0, palette 3
B8 53 03 20 - Dynamite, X: 20, Y: B8, palette 3
38 54 01 4C - Dynamite fuse, X: 4C, Y: 38, palette 1
40 50 03 48 - Dynamite, X: 48, Y: 40, palette 3
48 51 03 48 - Dynamite, X: 48, Y: 48, palette 3
40 52 03 50 - Dynamite, X: 50, Y: 40, palette 3
48 53 03 50 - Dynamite, X: 50, Y: 48, palette 3
78 54 01 5C - Dynamite fuse, X: 5C, Y: 78, palette 1
80 50 03 58 - Dynamite, X: 58, Y: 80, palette 3
88 51 03 58 - Dynamite, X: 58, Y: 88, palette 3
80 52 03 60 - Dynamite, X: 60, Y: 80, palette 3
88 53 03 60 - Dynamite, X: 60, Y: 88, palette 3
28 54 01 CC - Dynamite fuse, X: CC, Y: 28, palette 1
30 50 03 C8 - Dynamite, X: C8, Y: 30, palette 3
38 51 03 C8 - Dynamite, X: C8, Y: 38, palette 3
30 52 03 D0 - Dynamite, X: D0, Y: 30, palette 3
38 53 03 D0 - Dynamite, X: D0, Y: 38, palette 3
E7 FD 00 20 - Blank sprite
E8 FD 01 10 - Blank sprite
F8 FD 81 10 - Blank sprite
E8 FD 41 24 - Blank sprite
F8 FD C1 24 - Blank sprite
E7 FD 00 40 - Blank sprite
E8 FD 01 30 - Blank sprite
F8 FD 81 30 - Blank sprite
E8 FD 41 44 - Blank sprite
F8 FD C1 44 - Blank sprite
So, it appears that Gyromite uses 8x8 sprites. Sprite tile #$FD is blank, and it appears quite a bit on the screen. Perhaps "things" can be manipulated somehow in some way so that you can fit in an extra 2 tiles for each turnip.
There are a few blank tiles available in the CHR-ROM for sprite graphics.
From the way the turnip related data is set up, it seems that there are a maximum of 3 turnips in each level. So, there should be room (at least, in theory).
An idea for a Mario-related change could even be the vegetables (Veggies/Sprouts).
However, a consideration that comes to mind is a potential risk for sprite flickering.
There are other people more experienced with this area who could probably help you out more with this than I can at this point, if it's really something you choose to look into. However, hopefully this can help you and others get started. As always, best of luck.