Painters tape jigs like this are really handy, they definitely have their place. Great tip.
However, if both high accuracy and repeatability is necessary you’re going to run into problems for two main reasons.
1, on power up the Glowforge calibrates itself all over again. This will lead to slight variations in your zero position.
2, your tray has some slop. The divots don’t hold it absolutely in place. You can eliminate some of this by using @timjedwards’s tray boots (search the forum for them), but that won’t address #1, nor will the position hold if you have to remove and reset the tray, boots or not.
Of course this is only an issue if you need extreme accuracy, as in kerf-width or less. For most things this isn’t an issue so your tape method Is quite enough. If you do need that sort of accuracy, traditional one time use jigging is more successful.
As an aside, once you junk up the Glowforge from lots of cuts you can often see the cuttable area just by looking at the dirty parts of the tray.
As for your quarter inch Baltic cut problems, not sure how you tested but this method usually gets me on track: