"A"
treat the old app as guidenace on what the spec is but not more than that.
you have major changes to make and the old docs are not any good given what you say.
there are times when a fresh start is best, then you can dump the trash and work clean.
PS:
workload and time constrains - you have two main options,
1) put in writing why you need to do "A" and ask them to do it, and if they do not want to then ask them to sign off on your responcibility for any and all errors / damages that may result for not following best practice in software design and development.
2) find another job.
harsh - yes. but if you are willing to take the blame then you need to be in control. if they refuse to budget the time and moeny to do it right then you need to have it in writing that they knew the facts and chose to not follow your advice.
then later when it is an epic fail or is buggy as heck you can step away clean or then have them pay the added cost of fixing it w/o you beeing under undue and unfair pressure.
if you do not get it in writting, if you do not raise the bar and make sure they understand why then when things go bad you are an easy scape goat. you get the short end of the stick not the manager who told you to do it.