Can I use a larger garage door motor as a substitute for proper springs?
Absolutely Not!!!

Garage door openers are not designed or intended to hoist the door by brute force - the door should always be adjusted for easy manual operation before the opener is connected, or in the event of the opener failing, a power outge, etc.

This is primarily a safety issue (getting killed or injured by an improperly balanced door crashing down) rather than a "how powerful is the opener" issue. Openers are not intended to hold a heavy door up by brute force, and will probably shear the (usually plastic) gear teeth under excessive loads, leading to the door crashing down and possibly injuring/killing someone.

Get the mechanicals sorted out (use a reputable company, not a guy who does a poor job), or have the whole door replaced (I'm fond of a nice insulated steel door, myself) with a properly suspended door that can be easily operated by hand. Then connect the opener to it.