Many questions.
15V load regulation - first determine whether this is a prime
feedback or cross-regulated and regulated "secondhand".
You can't expect perfect regulation when it's not the fed-
back quantity itself. Look at ground rise (return current)
and its contribution to feedback error, and whether the
feedback voltage divider point is or is not staying as-set.
Spikes, you need to be clear about their nature. Spikes
every cycle may be due to a combination of too much
inductor interwinding C (HF shoot-through) and poor or
mis-located or too little HF filter caps, where you need
a very low ESL to make the caps effective against the
interwinding capacitance. But a stiff decouple to a
spikey ground can put the ground noise onto the output
too; ground needs to be real solid. Too much capacitance
on the switch nodes can really bounce the ground; if the
spikes are only on the HL edge then look to ground quality
and Cout of the PWM and the power stage. I think if you call
your output filter a "proper snubber" maybe it's not as proper
as you believe.
LM1117has a rec max 15V, abs max 20V input rating. You
don't say which supply it's powered from. Maybe your
spikes plus set voltage exceed the rating.