This may or may not be related:

I under/overclocked my DMG (with EMS) so far with a thumbpot and LTC1799 (no kit, straight balls) that I wiped my cart clean. I had to clear the cart and start over.

Have you tried changing the cursor repeat settings?

My LSDJ Cursor is really fast, Is this a good thing?

When I mentioned the cursor speed I meant after I switched the cartridge out to a stock gameboy I found that the number value in the cursor refresh setting was something really high, like 4C (not the exact value, but a estimation of what it actually is without turning it on and checking).

Alright, I'll try this on the cart that crashes the most and see if it fixes it. (my cart with up to date software is working fine after using it on a stock gameboy and resetting the corrupted Sav data)

I own 2 EMS 64 carts along with a precision clock modified DMG.
I remember (on 4.6.4) that I use to get errors and all sorts of buggy things when I chose to alter the clock speed.
I tried to recreate the problem (on 4.6.5) just now and everything seems to be running swimmingly.

My best route of attack for your situation would be as follows:
Backup .Sav data is on the cart, upgrade software if you haven't done so (reflash isn't a bad idea either). After that then proceed to reformat the LSDJ by going to the project menu with the cursor over 'load/save song' and pressing Select+A buttons simultaneously. When asked "Really?" click yes, when done the cart will be empty of saved songs.

works fine on underclocked units.

the slow nature in the way LSDJ responds in your underclocked gameboy is fine.  underclocking slows down the processor speed, you are seeing/feeling it in the slow response. 

if you slow it down enough, you can see the screen refreshing itself (pulsating sort of). 

bear in mind, changing the clock speed is taking the gameboy out of its designed-for operating parameters.  so a lot could go wrong i suppose, but i know for sure these carts work fine on underclocked gameboy, whether with a real crystal oscillator or with something like easyCLK. 

the scrambled logo on start-up seems like a edge connector contact issue, most of the time a blocky logo comes from this.  as cliche as it is, blow hard into the game slot and the cart's connector, and try again.  thirty, forty times as its been said....

hmmm, only comment i have is that i use a 64mb ems that i swap between my underclocked gameboy and my stock one and i never have a problem. thats a bummer yo.

I've had a problem with two EMS carts that I've used with underclocked gameboys- the first was an underclocking I did with a slower crystal, the second was with an easyclick. After using the cartridge with an underclocked gameboy the cursor move information gets erased and it is set to a really slow setting. Often times the cartridge boots to the nintendo logo with a block missing, or with scrambled text.  LSDJ is installed on both pages of the cartridge. If it boots then it works for a few minutes at a time then crashes. New Sav data does nothing to fix the issue. Anyone encountered this before?