What's your favorite $5-7000 turntable?

Woodpecker is a good choice but think the Stabi R is even better IMHO. Strengthen your wall mount and don't look back. 

For a decent turntable that can work well with your Schröder tonearm with reasonable weight to be placed on Wall mount, I would suggest Roksan Xerxes 20 Plus or a Used Roksan TMS2 or TMS3, these relatively new Roksan do not have the top panel sagging problem. If I have more space, I am sure I will get one of these to match with my Zeta tonearm....... I am using a Micro Seiki turntable with FOUR tonearm, and planning to setup a Denon Direct Drive, these turntable have taken up all my three Audio Rack Top platform........ 😅

I really like the Feikert Volare which can handle one of the higher end Origin Live arms like the Illustrious or Conqueror. Compact, well built, sounds good. Not sure if the Pure Fidelity "E" series (Eclipse or Encore) can be had within your price range but I like these better still. I've got my PF Harmony on a wall shelf and it fits nicely. 

Pure Fidelity

In my main system I'm using a Michel GyroDec that I bought in 1983. It has a Linn Ittok LVII arm with a Grado Reference Sonata. The Gyro has been brought up to the latest specs. My secondary TT is a restored Thorens 160 with a Rega RB330 / Ortofon 2M Black. Very happy with both tables!

Rega P10