I would check out Hugh and Crye. They're in your price range (their shirts go as low as $65 - $85 when not on sale, cheaper if you find a sale). They are not true made to measure but they have a wider variety of fits from skinny to broad, and short to tall, (basically skinny, slim, athletic, broad are their torso cuts and they go short, average, tall for the length and hence you get 12 sizes and a closer to MTM fit than most mainstream retailers.

Another option would be one of the MTM online outfits - Ratio or Proper Cloth. I have one Ratio shirt (classic white broadcloth dress shirt) that fits really well - I save it for when I have to look really sharp. It took one back and forth to get the fit dialed in properly but once that happens you can get multiple shirts made that will fit really well. My recollection is that their shirts start right around $100 so they're in your price range but a little more than Hugh & Crye. I chose Ratio over Proper Cloth first because they are, or used to be, a sponsor of Dappered, and also because (if memory serves and they haven't changed things) their shirts are sewn in the USA.