Can I remove a cemented post & crown and re-cement it?

My post and crown fell out last night. I cleaned, rinsed and dried both crown and area where the root canal had been performed. I used a packet of dental cement I'd gotten from my dentist 3 or 4 years ago when the initial work was done (a 2-part expoxy like cement). Unfortunately, I did not seat the crown correctly and my bite is off. It is driving me crazy. The dentist who did the work is no longer around and I do not have dental insurance or money to pay for fixing this. Is there a way for me to dissolve/remove the cement and try re-cementing it? I had put the crown back in (before putting cement on) to make sure the fit was correct and I would be able to cement it in place correctly without any issues - not sure if there was a bit of cement in the way or I worked too slowly that cement dried as I was inserting the posts/crown but definitely off. Afraid of doing damage to other teeth, jaw or tongue due to incorrect lineup. Any suggestions?