1) Use Mic Pre (my friend uses Universal Audio 4-710d for his vintage synths)
Yes, do this as it solves all your problems.
2) Use a DI unit to convert/boost the unbalanced signal to balanced
A DI does not exactly do this. It converts a high-impedance unbalanced instrument source(which you have) to a balanced mic-level source(which you still need a preamp for)
3) Input everything directly to the -10dB inputs in HD I/O and adjust the gain input on each channel. I haven't tried this yet but I'm guess the HD I/O has enough headroom to boost the signal
Read the manual that came with your HD IO as it says very clearly that unbalanced connections MUST NOT ground the cold side(which is exactly what happens when you plug a standard TS cable(as you would use with most drum machines and keyboards) into a balanced TRS patchbay. I would use a preamp, but the 4-710D might be pricey for this purpose.
Having said all that, you could save lots of cash and use something like SMPro's EP84. http://www.smproaudio.com/index.php/...s/preamps/ep84
One last option; if you are good at soldering, you could make "quasi-balanced cables to connect your unbalanced keyboards to balanced inputs(the -10 inputs on the HD IO), but these need to be wired correctly. Using balanced cable(assuming white and black wires, plus shield), connect the unbalanced end as tip=white, sleeve=black(do not connect the shield at this end). At the balanced end, the TRS plug would be tip=white, ring=black, sleeve=shield.