Bear with me here...

Steerer OD = 25.4mm
Crown Race Seat = 27.0mm
Crown Race Seat Height = 5.0mm
Head Tube ID = 29.5mm
Steerer Length = 182.0mm from top of crown race seat/187.0mm from bottom
Head Tube Length = 145.5mm
Difference Steerer - Head Tube = 36.5mm

So, it sounds like I have a 1" JIS setup, right?

What is an acceptable stack height range for headsets for this frame? Thanks.

yes, 27.0/30.0 (29.5 for interference) is JIS.

Stack heights vary by brand and model. But IME the stack height of any model is the same whether it's the ISO or JIS version. There's no set height, with some models being in the low 30s and others as much as 45mm. Unless otherwise instructed I cut forks for 45-46mm stack height, and use spacers for shorter headsets. That allows for a change to a taller brand later on.

+1 FBinNY's comments.

Keep in mind it is the fork that determines the maximum stack height you can use with your frame. The difference between the length of the frame's head tube (measured from top edge to bottom edge) and the length of the fork's steer tube (measured from the base of the crown race seat to the end of the tube) will give you the maximum stack height you can use. You can use a headset with a lower stack height simply by adding spacers, but if your chosen headset has a stack height greater than what you have measured on your frame and fork it won't work unless you replace the fork with one having a longer steer tube. The 36.5mm you have measured on your frame/fork is right in the middle range of stack heights for popular headsets, so you should have little problem finding one to work, e.g. the Tange "Levin" is nicely made, available in JIS and with a stack height of 33.5 ought to work fine with a spacer or two.



Source: Barnett's Manual

So you can use any headset with a stack height less than 41.5mm. This is on the longish side, and most popular headsets will work.
There's a bit of wiggle room here so you can use a headset with a stack height of up to 42mm with no issue, and 43-44mm if you can eliminate a washer, but consider this plan B at best.

I forgot to add one thing - I'll be installing a headset brake hanger for cantis. I just measured and this will act as a 5mm spacer. Can I still go with the Tange Levin (which was what I was planning to order in the first place)? From what everyone's saying, the answer is "yes" - stack heights that are too long are bad, but stack heights that are shorter than needed just require spacers. Right?

Right. You're always safe going with a shorter headset. +1 on FB's 8:49 post -- if you can, leave the steerer long enough to accommodate a "tall" headset later on.

Also, read this by Lennard Zinn on brake shudder before you commit to a headtube-mounted brake housing stop.

Yes, it's like cutting wood. you can always cut shorter, but cutting longer is seriously difficult.

You'll see that I found you 5mm more stack height, so you can use any of those 36mm headsets + your hanger if you want.

However, many people find that crown mounted hangers offer better brake performance, so you might want to go that route and use a 5mm spacer on the headset.