The MR16's are quite small and have a similar output to your torch. You can get all sorts of colour tints and beam angles. Basically 4x 3W will draw 1A form your 12V battery, so your battery will last a very long time. Here is a photo of some I bought to put in the garage as emergency lighting (can and ruler give you an idea of size).
The strip lights can get warm but only about body temperature normally. I would mount the strip on a length of aluminium so that they can be adjusted and give you a surface to mount on, it would also act as a heat sink to be sure to be sure. Your brolly will be safe.
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