Cree LED in a small plastic diffuser, also AC to DC converter

I want to build some constant light source for my building's stairway (just near my appartment's door).

It would feed from a "12V" AC source of the doorbell (which is a very simple box that now feeds only a 12V 1.2W incandescent festoon). Readings with my multimeter reveal it is only 8.5V AC and 55mA, so about half a watt there.

The box and current bulb can be seen here:

I tried replacing the incan festoon with a LED one (this one: ) but the contacts where too big for the box.

When I used it with the 12V source of the doorbell, it flickered pretty badly... maybe because it expects DC instead of the supplied AC, or because of the lower voltage it received.

I thought of putting some cree emitter (maybe XP-G for efficiency and more floodiness initially?) inside one of these diffusers, above the doorbell box:

http://www.goodluckbuy.com/index.php?target=products&bid=42&sl=EN&aff_id=9128&product_id=64003

It needn't be more than 50lm, I think, but the more lumen the merrier.

For about 50lm, the XP-G R5 needs to be fed with about 120mA, and for 140lm with 350mA. Do you think these tiny diffusers can withstand 1W LEDs?

I will also need to reduce the "12V" input to about 3.5V-3.7V. Should I use a resistor and live with the flicker or should I use one of these converters and hope for the best?

This one gives 600mA, seems to be too much (about 200lm by Cree's specs): http://www.goodluckbuy.com/1x3w-600ma-led-driver-power-supply-transformer-12v-ac-input.html

What do you suggest I should do?

I'd have a go with the AC/DC, it's output will depend on what the supplied input can offer current wise.

The diffusers should be up to the job unless they have done something very wrong when making them!