The wing would have to be strengthened so made a lot heavier. With the current landing gear the weight could only be increased to 287t or so. Using the standard fuel tankage and that Higher MTOW, it would only get a range marginally longer with a 232 or 254 pax load, but most likely shorter if you factor in that the structural strenghthening and engines would add at least 10t, (the weight difference of the engines alone is 9t!), to the OEW along with the higher rate of fuel burn. If you used the -500 wing you can add another 20t for the wings and undercarriage. Without using the -500/600 wing and undercarriage the engines would strike the ground.
You have to remember that the Trent 500 engine is larger in phyisical size than a GE
CF6 or a PW4000 used on a 747 or 767. It's also heavier than those engines by .5t per engine. And it would be almost impossible to match the cruise thrust of 4 Trent 500's (10,700lbt each) to the slower cruise speed of the A342 unless you fly it at a lower altitude througout the Mach .82 cruise.
As for competing with the 7E7-9. The 7E7 will have fuel burn rates very near the 767-400 around 4.5t/hr, but an A342 already has a fuel burn of around 6t/h. And this Trent 500 A342 would burn fuel at at least 7t/hr. Remember also that the MTOW for 7E7 will be 227t. The MTOW of the A342 is already 275t and this new wing, new engine A342 would have to have an MTOW of at least 300t to start with and may not make the 7E7-900's range at that weight.
This was a very interesting suggestion, and excercise for me, but Airbus is already pondering a 7E7 competitor, the A350. If it comes to be it will be a twin with increased MTOW over the A332 with larger engines of close to Trent 900/1000 size and thrust. But without a new wing an A350 would be slower, Mach .82 vs .85, (if it used the same fuel it have a 300nm shorter range), and without the advanced composite construction it would be much heavier than the 7E7 is going to be. We'll have to wait and see what Airbus does about the 7E7 threat. So far there are not really any specifics that have been made public.