I've got a Lee Loader in .32 Win Spec/.32 Rem. (Found it a gun show for $5.00) It states that not only the tools/dies are good for both .32 Win Spec and 32 Rem,, but also that the data is good for both .32 Win Spec and .32 Rem (the only difference between the two is that .32 Win Spec is rimmed and .32 Remington is rimless).
Here's the data from the Lee sheet:
All loads are for 170 grain .321 flat nose bullets and Large Rifle Primers (DO NOT USE MAGNUM PRIMERS)
Max Trim Length 2.040 in, 51.81mm; Max Overall Length 2.565 in, 65.15mm
Powder Grains Approx Vel
IMR3031 28.9 1900 fps
IMR4064 29.5 1750
IMR4895 30.2 1850
IMR4320 30.7 1800
HodgdonH4895 30.2 1850
Win 748 33.6 2100
Please double check my data from other sources as I've been known to mistype. There are other loads for .32 Win Spec listed on Hodgdon's website. (that use Hodgdon, IMR and Winchester powders).