Loosening the rear band won't do anything as the threads are on the same side as the head and the rest is just a post.
Front band is a different story however.
You have several issues that can cause this, try the front band screw first. Marlin has NO torque specs for any of the screws, so over tightening does happen. If it's been cranked on hard, it may have squeezed the front band a little out of shape.
Next, check the tang screw and stock fit. make sure the stock doesn't have any play. If it does the first shot bumps the stock into position causing that shot to be a "flyer". You'll either need to tighten the screw, or bed the stock and receiver mating surfaces if tightening the scew doesn't work.
Might be a scope issue too. Try this. take a shot move your scope 8 clicks up, take a shot. Some scopes with a mfg defect actually take one shot to cause the crosshairs to "settle" after traveling or after being adjusted. Or see if the same thing happens with open sights.
I'd HIGHLY recommend "Accurizing the Factory Rifle" for any one with a lever gun shooting large groups, having vertical / horizontal stringing issues, or flyers. 99% of the fixes discussed can be done at home.
Half the book covers levers and or single shots with 2 piece stocks. Did wonders for a 30-30 for me.
Last, post your question on the Marlinowners.com forum. Lot's of experience there.