Be aware that many of the parts other vendors (like Ames) sell are the same ones that you get through thepartsplace. I found that out when I bought some of the plastic lower dash inserts for my 69 from Ames and saw that on the back side they were clearly stamped "thepartsplace". Even so, sometimes Ames has the same part for less. I guess it has to do with their cost, volume, and shipping charges.
The best approach would be to select a few vendors that you're interested in, then call them and talk to them about the part(s) in question. Sometimes they'll tell you the source, sometimes not - but they SHOULD be willing to give you details about how the part is made (is the outer finish plastic or padded vinyl, for example).