A couple of easy outs:
1) The "beaming through shields" thing is simple to justify by saying that the shields were down. We know that there were a lot of cuts in the scene where the E-D flies from the star to the outer wall; a great many dialogue-specified minutes were compressed into just a few filmed seconds. There could simply have been a cut where the shields of the transport were dropped and the two heroes were beamed out, and then Picard had the torpedoes fired and the camera showed them streaking towards the re-shielded ship and blowing her up.
In other cases where our heroes are accused of beaming through shields, the enemy is typically waiting for his chance to fire at the temporarily unshielded ship. Here, though, no harm would come from briefly dropping the shields; the doors of the Dyson sphere would merely close by a few percent more, but still remain sufficiently open for our hero vessel to barrel roll through.
2) People staying conscious within the transporter beam has always been the preferred option, considering how "transporting" is really done in Star Trek. It consists of two separate shots, after all: "before" and "after". And those two can never feature the character in exactly the same position, not unless the character is computer-animated rather than played by a live actor. So we should always assume that the character can move about while gripped by the transporter beam.
"Gripped by beam" isn't what the associated technobabble suggests, anyway. Transporters are supposed to move the transportee from our realm to another, "phased" one; there is no rule that would say that movement in the phased realm is forbidden. All we know is that movement in that realm can take place through walls, long spans of vacuum, etc. Just like in "The Next Phase"...
However, one established feature of this phasing process is again due to the way "transporting" is filmed: the transportee does freeze for a split second at the end of "before" and at the beginning of "after". Since Scotty was said to have locked the transporter on a special mode that surprised even LaForge, it's not difficult to claim that this mode utilizes that temporary freezing effect to stop Scotty from having a metabolism and losing 75 years' worth of body fat.
3) Starfleet is in the habit of giving away its ships. Or shuttles, at any rate. (And that's a rather high rate!)
Many a plot complication involves the sacrificing of a shuttlecraft, often for the most trivial of reasons. Apparently, this type of hardware doesn't cost anything much, and can be freely expended if it saves even one life, or serves as a convenient distraction, or just plain makes Worf happy with his daily dose of kaboom.
Timo Saloniemi