"child-pays-for-parent (CPFP)" Not a term you hear about often but that's what it is, and it is permissible because the block considers two sequential transactions valid so long as they appear in the correct order in the block.

To avoid having to do it twice, like the second link mentions, just make sure the fee rate on the second transaction plus the first divided by the total tx load is enough to keep it in the next block. Not sure how big the second spend is, maybe 2/3 the size of the channel open, so the average of both versus vBytes is how you ensure it gets through sooner. It would be handy to have a calculator for it.