There's a short bolded TLDR summary near the end of the post. For anyone that doesn't care for long winded posts.
Anyway, testing!
I made use of the notes on testing crit rate on the BG wiki crit page. Basically, you push crit rate close to what you think will be capped and test until you get a non crit. That shows that you aren't capped, so you increment upwards.
And normally this would take a really long time to test on a WS. cause we're talking hundreds of WS. But since Shining One makes any Polearm WS crit... well. XD

Using Sonic thrust to gather mass samples each WS made things a lot easier. I felt very smug for having thought of this. lol.
Also I found that only 15 mobs worth of WS would actually display. If I pulled any more than that it wouldn't show the rest, and I was potentially missing the non crits. So I had to redo a few tests.
Now, I did a lot of tests working up to and sometimes overshooting the actual crit rate, but I'm only going to include 3 of them, and technically only two are needed to prove the 3k TP crit rate+ with a high degree of certainty.
But first a bit on conditions and crit values.
Razed Ruins: 30%
Base crit rate: 5%
capped dDEX: 15%
Merits: 5%
And then varying amounts of crit+ gear depending on the test.
I used Voracious Violet and Sea Daughter atmas + spirit link(Wyvern TP battery) to get TP without having to kill my test mobs doing it. Spectators are really squishy. I typically had 3K TP before I even finished pulling and lining up the mobs.
Non Crits were really obvious, being like 20k dmg less than the crits. And I didn't have to worry about multi hit messing with the dmg since the first hit always killed them. Whiffed first hits that landed a multi hit proc only hit like 6.7~7.1k. And I honestly didn't think about one of them being a non crit until this very moment. Thank you logs. None of them varied enough to have been a non-crit. And thank you Razed Ruins for making the crit/noncrit difference huge.
All test WS were done at 3k TP.
Crit+83% test:
58 samples
1 non crit.
Crit+84% test:
182 samples
1 non crit.

This test shows that the crit bonus from shining one must be lower than 16% Else we'd already be capped.
EDIT: I derped really hard, and used the numbers and screen shot of the wrong damn parse here initially. I had 2 very similar tests... Corrected.
Crit+85% test:
309 samples
0 Crits

And this one shows that we very likely are capped. The chances of going 309 consecutive hits without a non crit even at 99% crit rate.. well, I honestly don't know how to calculate that. But it's pretty damn low. I thin the BG wiki page on crit rate I referenced earlier has something on the probability.
TLDR: So, Shining One grants an additional 15% crit rate at 3,000 TP. 1k and 2k are untested, but very likely 5% and 10%.
Keep in mind that this is just the bonus from TP on Shining One. You still get the effects of base crit, merits and dDEX. So you're looking at a 25% chance to crit on WS with 5/5 crit merits, floored dDEX, and no crit gear. That's your minimum at 3k TP. And probably 20% at 2k TP.
Hopefully this will help anyone trying to calculate Shining One's DPS and avg ws DMG. PS. I'd love to see some updated DRG spreadsheets/sims. <,<