An injector leaking down into the manifold will also bleed the line and
make starting difficult. A cheapo fuel pressure gauge will at least say
if it's a leakdown problem.
But you can also get cold starting problems from plain overenrichment,
which is a consequence of some mods (needing cranking VE table work
along with the main, and maybe some pulling back of cold EQ table
values). If the line stays pressurized and starting still sucks that says
it's a tune issue.
You could pull the whole injector rack and put it in a pan, prime the
line and look for drooling while the pressure gauge is on there. Drop
and no drool implicates the check valve; drool in the pan means new
or reconditioned injectors. You'd have to find a way to keep the
injectors from popping out - a junk LS1 manifold would do, could be