The heaviest part on my bike is the bottom bracket. Along with the other parts needed to convert my touring bike to a single speed, how much am I looking at spending? I'm guessing up to $150. If it's more than $200, I'll just buy a single speed.

remove dérailleurs and cables, shorten chain to fit desired gear combination... et voila single speed, no cash. If you like it, try replacing the gear cluster (if it's possible with your rear hub) with a freewheel (prices vary), redish the wheel, buy single stack bolts for the chainring (prices vary) now it also "looks" like an "authentic" single speed.

I think the heaviest part of your bike is probably the wheels, or really the frame, but who cares?

Sell your 610, for about 150$ on CL. Save up to get a comparatively sub-par (but pre-built) single speed bike from one of the many online sources now available for around 300-400$.

unfortunately, i'm in Vancouver, CA where single speeds (good ones) start at CAD650. but i could probably get CAD200 for my Miyata. because of the age of the bike, i'm told the switching out of parts may be tricky, therefore driving the cost up. i'll take it to a bike shop and get an estimate since i know which gear i want.

Sell it for $250CDN on CL then order a bike from bikesdirect.com for $350 USD, drive down to the letter carrier in Point Roberts and bring it across. Done.

https://www.bikesdirect.com
https://www.thelettercarrier.com

I will say something constructive...

Miyata 610 is from the 80's, switching out parts shouldn't be hard at all, if you don't have the tools and whatnot, just bring it to OCB on Main st, they'll be more than glad to help you with the project.

miyata 610 is a desirable touring frame. Could get something like $200 for it in Toronto.

By far the heaviest thing on the bike are the wheels.
The BB can be kept or switched out and the cranks can also be switched if you want.

I would just spend your $200 budget on a wheelset from BWW or ebay.

One and done.

switching out parts on your miyata will not be hard... not only because, as I noted above, that there really are no parts to switch out, but also, because there is nothing unusual about the dimensions of that particular model. Mass produced, with standard shimano parts. You only need to get an adapter if you want to use stems for threadless headsets. I think your best option is to just order a new wheel-set (100-150$ usd), just make sure that the axle can span the dropouts appropriately (probably 130mm). The 610 is a decent frame and if you're already comfortable on it, you won't be able to buy another bike of equivalent quality within your budget.

What you need:
1: fixed gear (or flip flop) rear wheel, the front wheel you have now will work fine
5: short stack chain ring bolts.

Step 1. Remove the derailers, shifters, cables and rear wheel.
Step 2. Remove crankset, use new chainring bolts to secure single chainring to middle position of crank.
Step 3. Shorten chain, and replace.

Tada, you have yourself a new fixed gear, or single speed. Nine times out of ten, that's all it takes.