@Rolnar, I think the acid to acid chloride is faster than alcohol to alkyl halide.
OP, This is a case where you should just do it at reflux overnight and trust it. Thionyl chloride is a champ, these reactions are usually quantitative. If you want to give it a boost add a drop of DMF, its a catalyst for this reaction. Also, its very common to use thionyl chloride as the solvent for this reaction, so you get a huge excess fighting for you too.
If its not complete, whatever you do the next step (amine? alcohol?), it should be easy to use acid/base extraction to get any carboxylic acid that didnt make it
The alcohol trick might work though, just take a bit and put it in dry methanol. The acid chloride will esterify WAY faster than the ester under ambient conditions. Like... months faster. Ive never tried it for checking by TLC.