Do you think that we could get away with putting 0.3mm vias in the actual LED footprint, with spacing about 1mm apart?
Yes, but only if you have the board shop plate the vias shut (ie they will be totally closed). If you don't, the solder paste when in the infrared/vapour phase oven, will be wicked down the holes thereby degrading the heat transfer to the top side of the board.
Use a 0.2mm solder paste screen to deposit a reasonable amount of paste under the LEDs.
Also, consider using 2oz copper if you can for much better heat dissipation.
We have had a lot of production experience with SMD mosfets, even to the point of having x-rays taken of the resultant solder paste spread under under the mosfet heatsink & the above is what we concluded brought about the best reliability.