No one going to tackle this one huh? OK... I've got time on my hands, so here goes.
You're a brave man deckard. At least you went into it eyes open, but the flip side is that your expectations might be a bit lofty.
Cheap guns frequently have cheap gun issues... the money saved may be spent trying to bring it up to decent gun specification. As some will say, "Buy best, cry once. Buy cheap, cry often".
1. "Spongy" is a term seldom associated with the 1911.
- You can have free play where the trigger is literally not bearing against anything... this is a poorly fitted element of "pre-travel" and can often be associated with a trigger "bow" that is under length or a out of spec frame.
- You can have excess pre-travel... where there is additional free travel, but there is resistance. This is prior to actual contact with the sear. This is not a bad thing, but can be annoying on a range/target gun. Too little pre-travel and you can have trigger reset problems.
- You can have too much or not enough spring resistance... primarily a function of the sear (leaf) spring adjustment.
- You can have "creep", which is the period when the sear is releasing the hammer... and it seems to take forever. Long hammer hooks and a sear with little to no secondary angle will create this feel.
- You can have a gritty, crunchy feel associated with poor sear and hammer preperation, engagement and fit.
- You can have excessive over-travel... after the sear has released the hammer. A trigger without over-travel adjustment that has been poorly fit, a trigger with over-travel that has been incorrectly adjusted or a grip safety where the vertical angle on the release arm is cut too far back... in lieu of a proper trigger over-travel set up.
Pre-travel and over-travel can be adjusted with the appropriate trigger component.
Creep, grit and the distance of trigger travel required to release the hammer upon trigger to sear engagement can be corrected with proper fitting.
2. You may be able to correct much of this with a properly fit barrel bushing. I suggest obtaining a custom, "sized to order" one from EGW. If on the other hand your misalignment is from poor lug fitment or mis-machined parts... you may have bigger problems. If, for example, the bore of the slide is machined off center or at an angle... you would need to have the slide welded and remachined by a highly experianced, 1911 gunsmith. If your problem is an out of round barrel, then it's best to simply replace the barrel.
Your cheap gun is getting expensive isn't it.
Trigger shaft? There are two elements to a 1911 trigger - the stainless steel bow and the (usually) aluminum shoe or pad... these last two terms frequently used interchangeably. The bow can be polished and even "adjusted" to obtain a better fit with other components. The shoe, on a new, aftermarket trigger will be oversize in the vertical direction so that it can be file fit to the frame for minimum clearance... about .0005"~.001".
The trigger bow rides in channels machined into the frame. These channels can be polished with the appropriate stone to remove burrs and high spots.
- You can purchase aftermarket triggers that are adjustable for both pre and over-travel.
- You can purchase hammer and sear "ignition kit" sets that are professionally prepared for best fit, engagement and release. They still may require fitting by someone who fully understands the 1911 fire control system.
- You can take your gun to a gunsmith and let them assess the issues and offer suggestions to correct them.
Do what you want... play with the sear and hammer, screw around with the sear spring... go nuts. But, remember, if your gun ends up being unsafe, do not load it, do not shoot it, do not aim it at anything you are not willing to kill.