Just a few comments.
Have worked on Sunbeam Tigers years ago, but know the tight squeeze the 289 motor is. Car came stock with a 260 2V (same setup as '63 Falcon Sprint) with a whopping 164 HP. The easiest spark plug to change on the engine was the #8 plug through a hole in the firewall behind the clutch pedal. The rest were knuckle busters.
The 260/289/302 engines are the same family, and share the same exterior dimensions. The 351W is a larger engine. It shares some of the dimensions of the 302, and some parts interchange.
A 302 would fit dimensionally, but I'd mock up all the accessories on a stand before installing it. Same deal with swapping heads. Make sure everything bolts up with the right size mounting holes in the right places.
Head wise, I'd look at the GT40, or AR165. You will have to pay close attention to the valve train setup so that everything fits, and works. Roller rockers are out, but Comp makes some improved factory style rockers that will fit under your stock valve covers. If your new heads use guideplates, you'll need hardened pushrods, and carefully check rocker arm geometry. These issues should be dealt with by your head Mfg. If AR, their tech support for this should be quite good (what will I need?). Both intake and exhaust ports are in stock locations so everything should bolt up there. Aluminum dissipates heat better than iron, so you're not adding any heat stress to the cooling system.
To add some torque, consider one of CompCams retrofit hydraulic roller cams.
The radiator by now must need replacement, and a good radiator shop could build you a thicker core. Or go with an aluminum one. Definately use a bigger fan, and your little 289 should cool quite well.
An
oil cooler would be a complete waste of money, but a baffled pan and windage tray would be worthwhile. For those kind of revs, use a billet steel flywheel, and SFI balancer.
Original Tigers (if I recall) came with 13" wheels. What size wheels do you have on the car now? This may be the biggest limitation of how much power you can actually use.
Good luck on your restoration. Tigers were fun cars. Damm shame the Mopar 340 wouldn't fit when Chrysler bought out Sunbeam and killed the Tiger.