This link should work. I think this is the one RF Head meant
http://www.sp2dmb.cba.pl/70e/PA70H_eng.pdf ?
I agree that this is logical, as the input match seems problematic, but also wonder the following.
Ogrevorbis, were you monitoring the Gate voltage, as well as the Drain current. If so, did you notice the gate voltage where the FET started drawing heavy current ? The reason I ask: the RD70HVF1 should draw next to nothing, until the Vgs reaches about 2v. Over 2v the current consumption will rise rapidly (see Vgs-Id characteristics top right of the attached). So depending on Vgs at the time, it could be related to DC conditions; it looks like you probably have quite a wide sweep on the bias pot. On the other hand, it could also be the increasing gain - with increasing Vgs, causing it to take off. As you said it's also drawing high current sometimes when you tune it, that could also be symptomatic of some kind of self oscillation. Were you monitoring the output in any way - other than power measurement. Wondering if there was any indication of "nasties" when the current shot up. I know you freely admitted that you don't have a lot of experience, are you confident in the stuff like grounding and layout ?
Otherwise I guess just try what RF-Head suggested, and report back. Even if it is taking off, if the input match is as bad as your SWR measurements suggest, it could be causing or contributing. On the other hand, if something is causing the driver to take off, it could be trying to drive with nasties, which could also explain a bad SWR which doesn't respond to tuning.
EDIT: Unfortunately the units don't seem to show in the datasheet. The horizontal axis is Vgs in 0.5v increments. The Vertical axis is Ids in 1A units. Again, this is the graph at the top right of the page.
You do not have the required permissions to view the files attached to this post.