I'd try double-sided carpet tape (Toolstation and elsewhere). It's slightly thicker than d/s Sellotape, and that gives it much better adhesion. If you only stick one edge it will allow your 7mm boards to move, which they probably will try to do. Obviously it's really a bit wide for your application, but with care you might be able to slit it lengthwise (depending on the lengths of your T+G).
The other stuff I've found to be good (so far) is the d/s tape used for sticking faux glazing bars to UPVC windows: I've been refurbishing the ones on the north side of our house this last year, as I've come to them whilst painting the house. Ours were wrongly installed about 15 years ago - there should be a 1-2mm expansion gap at the ends that meet the frames, without that the bars are forced off the glass they're stuck to. Several bars had come loose, and I removed and re-cut several others on the SCMS. I bought the proper tape to put them back, and it sticks lik a very sticky thing. It's not as strong as carpet tape, because there's a thin layer of foam in the middle, but it is really good. The foam would help you, as it will stick better to the uneven wood surface.
I'll dig out the supplier if you need it - they do a range of industrial tapes - but it is readily available on eBay and elsewhere. I needed an odd size, which was pricey, but the thinner widths are fairly cheap and would probably do your job well.
Clean both surfaces with a good degreaser - Acetone is excellent and pretty safe. Xylene is also good, but nasty. Meths is nothing like as good but does work. If using tape, leave the melamine smooth, if using glue, I'd roughen it with something like 80-120 grit as a mechanical key (then clean and degrease).
Hope that helps.
E.