I've had 3 HMRs. Sold one and now have two Anschutz 1517 rifles. They are wicked accurate, one with Leupold Vari-X 3 3.5-10X and the other with a Burris 4.5-14X Fullfield II. I didn't intend to put the Burris on that rifle, but I had it on hand when the rifle arrived so decided to use it. It works great and much cheaper than your max budget; I paid $230. The Leupold is great and can be had for under $400. I've killed 100s of prairie dogs with it out to about 150 yds, but doesn't have the magnification you want. I also have an Anschutz 1502 17Mach2 with a Bushnell Elite 4-16X AO that works very well; cost me $350. Actually, the scope I intended to mount on the new HMR is a Tract 22Fire 4-12X with T-Plex reticle. It was on back-order and since I had a scope I decided not to wait. The Tract scopes are really great. I have 2 of them and if I wasn't so impatient, I'd have 3. Here's a link to the scope I'll eventually buy. The price of $194 is unbelievable for the quality you receive, both in product and service. NOT a Chinese POS. Here's the link.
https://tractoptics.com/all-products/22-fire-4-12x40-t-plex
I bought a Tract Response 4-16X which I just mounted on my new 6.5 Creedmoor, but may not have a cross hair that would be the best for your 17HMR. But, wow, what a scope for $424; that is shipped, no tax here in Kansas. They come out of Pennsylvania. Can't say enough good things about Tract Optics. I've owned a dozen different brands and have Leupolds on most of my rifles. But, the Tract Scopes rival Leupold and are much cheaper, which they do by cutting out the middle man. They market directly to the consumer to our great benefit. Let us know what you end up with.