Great topic. Hope you get some advice from others.
It could take months and months for needle palm to germinate and even the others, quite sometime. I normally just broadcast mine on a good patch of soil in a flower bed around spring and the following year most have came up.
The late Gerry McKiness who owned the original Neotropic Nursery germinated many a palm seed for decades. He told me once that the best germinator is an empty Coleman Cooler filled with well-draining mix, such as a combination of potting soil, peat moss or coconut coir, and perlite or coarse sand. Cut a hole in the lid and insert a drop cord with a regular bulb a few inches above the seed planting line. His famous words were "that will make them pop" That advice was from years ago and I have been tempted to try it. Water the soil only when needed.
Jake, today there are several ways to go using full-spectrum LED shop lights. They are the best lights for germinating palm seed because they are energy-efficient, long-lasting, and provide the necessary light spectrum at a low cost. Just hang the lights 6 to 8 inches above the seedlings and adjust the height as they grow. I think several growers here use that method.
Once you have plants growing, I like using a 'grow light bulb' from Walmart. Just screw the bulb into a lamp and position the light on the plant. The plant will survive just fine. Some plants will continue growing, others may bloom and I always use them in winter. Just my take and certainly no expert on germinating.