They'd already deliberately taken the transporter out of play for drama. If Disco couldn't get a lock because of interference, the smaller shuttles aren't going to be able to.
They couldn't use the weapons the way you suggest because Stamets had to steal all the power to keep the expanded shield in place. Though I'd be curious what the result of superheating methane in space is, now that we mention it. In the presence of oxygen it would burn, but I wonder how it would handle the vacuum.
As "unwinnable" scenarios go, this one was relatively well constructed within the confines of the episode. They handwaved away the transporter with technobabble, but that's a problem with the transporter even existing as a technology so we just have to live with it. But everything else in the scenario was at least believably limiting to the crews' options. Would it hold up to rigorous cost/benefit analysis? Probably not, but how often does anything Hollywood?