I know what you mean... I got a Geordie bitter kit for xmas.
I'm no expert, but I'm not sure about using the Bitter and Lager together... the bitterness levels in the kits are really designed for brewing 40 pints each, it would be easy to end up with something really too bitter. The two can kits will only have the relevant amount of hop bitterness for a 40 pint brew.
I have actually done two cheap bitter kits in one brew, but the kits were really very cheap ones (Vina Basic Bitter) and very out-of-date... The results were surprisingly good, if very much like a stout, but I suspect the age and quality of the ingredients may have tempered the bitterness...
Using 100% spray malt is the answer. I'm currently drinking a John Bull bitter kit which was made with 1kg of medium spray malt (no sugar) and Safale yeast. Despite using a cheap 1.5kg kit, its actually turned out very good indeed, tastes not unlike Mansfield bitter. I'd certainly recommend the 100% malt approach to improve a cheap kit beyond recognition.
As for hops, I'm sure someone more experienced will be along soon to help you out with this, but the advice I've had is to not tinker too much with the bitterness levels of the kit. You can add more hop flavour by boiling a few hops in some wort for a short time, and aroma by adding more as the wort cools, before straining and adding back to the brew.