You've solved most of this yourself from what I have read, but I hope this helps.
The resin you are using is medium viscosity. My resin needs to be at 40oC before it would be at the same viscosity of your resin at 25oC.
I can't find the hardener 3663, but I have a good sense from what I have read and you've said.
Providing pressure is important to the strength of the bond - it tends to be really important for plastics. The lack of pressure around the tips is a real problem. Perhaps it can be fixed using racket straps or similar? If so, you will be able to press at a lower pressure. Falls mentions a few things, so I'm sure he's covered everything.
The resin you're using is an ambient cure resin, its slow to harden. This means the core will have plenty of time to absorb the epoxy it needs, a bonus - depending on your view. It improves the mechanical properties of the core, but adds weight, and its a bit random. If you're concerned about the core being a little too hungry and potentially starving the fabric, you can mix and apply a few coats to the core in advance of lay-up - an hour or so before. Put in a warm place, so by the time you come to use the parts they have started to gel/tack. Ditto for the veneer. Taking this approach will allow you to managing the thickness of the laminate really precisely, as the pressure applied will directly effect the thickness of the laminate only. If you really want, this method allows you can play around with the different resin ratio's for the top and bottom laminate - small variations to compensate for variation in a fabrics performance (tension & compression).
Don't expect the veneer to be saturated as such, results are species dependent, you're only really just coating the surface. So its a mistake to think the veneer has become harder or waterproof as a result of pressing.
Heat is what you need, direct to the cassette. Something like this would be the a good option - cheap, effective, no controller required.
http://www.discountfloorheatingltd.co.u ... _price.asp
Edit: You have a heat blanket, if it just the one at the moment, still consider this as an alternative. Given a bit of a push it can hold 60oC, it just doesn't have the power to get there on its own.
They won't raise the temperature massively, 30-40oC using 240v, but you will have a reliable cure cycle as a result. Initially add enough pressure to consolidate the parts, wait until the epoxy begins to gel and add max pressure required. Ideally, you want to be a little ahead of the gel time, so you can press out any last air bubbles and consolidate the parts effectively. I suspect you will max out at around 30-35psi - but that's just a guess. Run a test.
Talk to your supplier about how long it needs to be in the press at 40oC. They appear to recommend 12 hours at 50oC for the PH3665.
Edit: Rule of thumb, plus 10oC, half the time. So that's 6 hours at 60oC. You'll need to find that balance between temperature and viscosity. Ramp up too quickly with too much pressure and control over the thickness of the laminate will suffer.
I thought about suggesting a hot box (post cure). Personally wouldn't until you are happy with the performance of the epoxy/plastic bondline.
Hope this helps.