VPI MOTOR PULLEY ??

I went out today and bought a metal turning lathe so I can make my own pulley.......It seem that if you don't want to spend your life trying to contact somebody that doesn't want to be contacted, then you might figure out how to do it yourself.....Its given me another viewpoint on some businesses like VPI and PRO-AC ......Its OK to buy a 1000.00 turntable but don't trouble them with the small stuff.......I will make my own out of brass and skip the plastic VPI ones......  Will

autospec, let us know how that exercise turns out.  Seems a bit extreme to go that far.  Sure hope you have experience on a lathe, not an easy task for the uninitiated.

pmotz,
it's not biggie, but you gotta be very good with numbers and math.
all you need is the brass rod, good mirror scale caliper, micrometer and calculator(optional) and cut at least a few pulleys with various curve radius and barrel size +- few micrometers to ensure proper speed.
if going automotive machine shop, request also to manufacture few sizes with provided engineering draft.
 

And don’t forget the pulley will need to be bored for an "interference fit" on the motor shaft: (https://en.wikipedia.org/wiki/Interference_fit) If it won’t go on the shaft, or falls off it, it won’t matter how accurate the OD of the grooves are.

Purchasing lathe (gotta be kiddin' right?) that can cut with proper precision pulleys will worth a descent high-performance car such as Bentley Continental Azure Coupe(yea somewhere in few hundred k), but going just to trivial automotive machine shop with proper engineering drafts will solve your problem for a lot cheaper. 
Brass by far isn't best material. The best one would be rhodium.

Barrel shape of pulley is optional, but important at the same time.
Belt can travel over the straight cut pulleys and stays still over the barrel shape pulleys.

For the round-cut belt the pulley should have radial cut of slightly larger by .015mm to ensure easy fit without much traveling up-down. Please note that if radial cut radius is smaller than belt, the belt will wrap larger radius of pulley resulting higher platter rotation.

For my Sansui FR 1080 I've ordered 3 pulleys. one larger by few mcm, one exact and one smaller. I did not change the radius of the barrel. I only paid $19.xx for such endeavor.

My math had worked for me the following way:

1. Deriving the radius of a pulley.
Platter pulley with diameter D must rotate at 33.333... rpm and 45rpm
Motor pulley with diameter d must rotate at (as in your case) 300rpm
and ratio: 

D*s = d*S

where D is your large diameter of platter and s is your platter rpm and 
d is your motor diameter with S is motor RPM. (4th grade math?)

2. Deriving a radius of the barrel shape pulley.

Measure smallest dimeter d, height of any available turntable barrel shape pulley H and largest diameter D; divide both diameters by 2 to get radiuses r and R respectively; draw horizontal axis on your sheet of paper and plot 3 actual size vertical axis, originating from any arbitrary point of the horizontal axis -- 2 of size r and 1 of size R with R sized axis staying EXACTLY in the middle of 2 r sized axis giving you exactly 3 plotting points. As you know geometrically you can draw a circle via any 3 arbitrary points and that's how you define radius.
Graphically plot another horizontal axis via tops of r-sized vertical axis; continue to plot the straight lines of any reasonable size on both sides. Where straight line and curved line meet, plot a tangent lines going towards center till they meet and... BINGO you've found the barrel curve radius!

You can also refer  to http://math.stackexchange.com/questions/213658/get-the-equation-of-a-circle-when-given-3-points
if you prefer to solve series of quadratic equations instead.