Hydraulic brake bleed fail - try again or replace? I bled and completely replaced the fluid on a set of Tektro Orion hydraulic brakes, using Shimano mineral oil.  Before bleeding, one worked a little bit, and the other didn't at all.  In my impression, these are shit brakes.
Problems while bleeding:

The fluid was dripping everywhere- when I loosened the bleed nipple to fill the brakes, the bleed nipple gasket was either locked on, or so loose that the fluid would just drain out of the threads while trying to fill it.
The lever bleed port is on the side (makes for difficult syringe tube angle) and, despite being screwed in all the way, was also very leaky.
I did not have Tektro bleed blocks.  I used the bleed blocks I had, which seemed perfectly fine.
I was thoroughly unhappy with how poorly the syringe hose attached to the bleed nipple.  I'm using the proper kit, but it would barely stay on- I had to hold the hose in place on the bleed nipple the whole time

Despite these issues, I was able to bleed the lines and top them up.  Upon securing the bleed nipple and caliper bleed bolt back into place, everything seemed fine.  After riding for ~100 meters, they were useless.
Repeated 3x, same result.
Questions and concerns:

Used shimano fluid instead of Tektro, but that shouldn't matter.
Can I remove the bleed nipple and screw in an adapter instead?  I would need to order one to do this.
Should I try to get new bleed nipples and caliper bleed screws?
My suspicion is that the gaskets are shot and I should replace them.  Is it worth the effort?

I'm a mechanic- but three senior mechanics told me to trash these brakes and replace them with a better model.  I agree with this advice, but the owner of the bike doesn't agree.  On the one hand, I don't want to waste my time on shit brakes.  On the other, I am stubborn and like to get things to work.  What would you do?  I'm feeling a bit hopeless about trying to bleed them again- I'm curious if I am missing some trick or technique to deal with really finicky bleeds.
Update:
There is excess lever travel - the pads just don't clamp on the rotors.  The pads are fine and don't need to be replaced.
I'm using a BBB mineral oil bleed kit.  I've ordered a better shimano and jagwire one.
I'm only going to answer an aspect of your question; you can apply it to your brake how you wish.
Firstly, Certain Tekro models are fiddly to bleed but also feel like they need bleeding if the pads are worn down, so if you haven't put new pads in, I suggest you do that first.
When something like this comes into a commercial workshop and this amount of time has effectively been wasted, there's a strong argument for replacing the brake, giving better value for the customer and putting the mechanic's time back into another job that pays the bills.
When you are in another scenario where conservation of materials is important and you are time rich, you can play with bleeding this as long as you like, though you may already have learned all you need to know.
Meanwhile, SRAM Level, Shimano's entry-level hydro brakes and even new Tektro brakes are easy to set up, easier to bleed and don't cost very much, especially when compared to a workshop hourly rate.