How much faith can I put in the home test I passed last Tuesday with faint lines in the evening?
The assays used by the labs for the initial screening are no more accurate or reliable than the home test kits (being assays themselves).
I'll be doing one the morning before the actual test.
Instead of doing one on the morning of the U/A, you need to do it at least 3 days before the scheduled U/A (using the first mornings void, as Diege advised). That way if you do test positive (no line at all in the T region), you can begin your creatine-loading right then and there in preparations to use the Dilution method, since it takes 2-3 days for the body to convert the creatine into creatinine (the end waste product thats found in the urine). Read up on the Dilution "sticky" thread for more info.

-OR-

Utilize the 3 days to find a synthetic sample (or clean person) to sub. For tips, read the Substitution "sticky" thread.