Well, you sparked my interest here. Just bought a pack of the 300gr Taipans a week ago. Haven't loaded any up yet though. Those I have are interesting - measure consistently 0.3744-0.3748 behind the cannelure, but 0.3755-0.3768 in front.
I also use Hornady dies for .375, so I'll look out for these signs.

Also checked some older Taipan .375 350gr RNSP [which I have used] - again, on size behind the cannelure, and a little over [though not as much as the 300's - .376 region] in front. These have been fine in my Win M70 - still doing load development, but low pressures so far.
Woodleigh 300gr PP came out consistently .3748 wherever measured, BTW.

I'd suggest firing a couple as a test, keeping a close eye on pressure indicators. Taipans have thin, soft annealed jackets and soft cores, so effects of the oversize should be minimal. Probably not even noticeable, unless you're running a maxed out load.

While reloading for my .375 H&H today, several bullets were getting lightly stuck on the way down from the seating die.

I was using Hornady "New Dimension" dies and the bullets were getting stuck in the floating seater.

The pulling force to get the loaded rounds out of the die wasn't enough to pull the bullets out of the case but left a shiny rub mark just after the cannelure.

The bullets I were using were Taipan 300 gr RNSP. I measured 10 bullets using dial calipers and they came out to .377 inch. I also measured some Woodleigh .375 235 gr PP and they were .374 inch.

I have loaded 20 rounds, is it safe to shoot them off or should I pull them apart?

call hornady
jeffe