Newbie RSVR Gen 2 owner charging issue

Hi Guys,
I bought a gen 2 RSVR 1000 about 3 weeks ago, I love it, however I went away to Turkey last week I've come back and it has stranded me twice with a flat battery after stalling out.
It stalled a couple of times before I left but I just figured it needed a service/tune.
I checked the VDC at the battery and no matter what revs its showing 12.25V and falling.
So, Ive had the fairings off and I've found that someone has already done the charging mod as there is a choc block wound up with electrical tape coming out of the Reg/rec and 3 (green/yellow earth) 2.5mm leads going to the -presumably- stator.
So, themod appears to be done (i've yet to lift the tank and follow it back as the mrs is giving me grief). The reg/rec is absolutely boiling after 30 seconds. Would it be safe to say that the reg/rec is goosed considering its getting hot and voltage- no matter what revs- is steady?
Or do I need to check the stator?
Do i check the voltages going to the reg/rec with the bike running?
Any and all comments are appreciated

thanks for the reply, checked battery while running, took it up to over 4000rpm stayed at 12.25 and slowly falling. I will solder it in the future, I just need to find out which parts faulty. I'm sending myself some info I can check at work today. I guess the next step is V ac between stator phases (with the bike running) at the choc block?

Well, sussed it. looks like my stator is fine, did a phase balance like I would on any induction motor all good - 0.2 ohms, voltage when revved rose to 67ish Vac phase to phase. looks like I'm only up for a reg/rec...hopefully. thanks sixshotdave for at least replying. seems a bit dead in here

Bugger! I've just bought a second hand OEM Reg/Rec from the same model off ebay for £45! I figured it was the safest bet.
Aprilia RSV1000 R (3) 04' Rectifier regulator Regler Spannungsregler | eBay
I looked at different types but there is too much conflicting info so I played it safe. I'll do a search and ask on FB