15ma is not right. maybe something is limiting you.
the last time I looked at current, I had a dmm in series with my lab psu feeding a 3 term reg (317 or 350 style). the dmm was on the 10A setting. I saw peaks of 200 or 250ma (roughly) during relay switches. and during bootup, it was 1.5A or even 2.5A. bootup can be harsh but every 3 term reg I've tried seems to tolerate it well and once the startup surge is over (2 secs, about) its down to 70ma or so, steady. the 250ma peak is the most I've seen and its usually far lower than this.
your numbers don't agree with what I'm seeing. I'm not sure why.
as for test points, I would solder short insulated wires (1" or so) onto the pin1 and pin2 5v wires. use those 2 wires as test leads for grabbers or aligators. and take ground locally, too, when you 'watch' things. the middle 2 pins are your best ground for taking readings.
the logic 5v should be steady and insulated from the relay stuff if you have your own private 'alt' power.
as for grounding, try to avoid any snaking or daisy chaining. think if there is a more direct way from some gnd connection to the real star ground. chaining is convenient but could also cause sharing issues. for now, for debugging, go 100% star grounding. the lcd1 gets a private black or green wire to its supply (s25 #1). the d1 gets its own private wire to ITS s25 (#2). the lcd1 gets a private red wire to s25-1(+). the d1 gets its own red wire to s25-2(+). the s25-1 and -2 are tied ground to ground via a ferrite. and try to keep red or black wires to 1foot or less, from lcd1 or d1 to its regulator.
see if that gets you some progress.


