You need a diag tool. The cost of a proper tool will be offset by not paying labor for repairs.
The Tech2 with the GM PCMCIA Linear Flash card a CANdi or a diag tool can command autobleed. I paid $300 for my Tech2 clone. Not sure how expensive they are now.
Supposedly the Harbor Freight Zurich ZR13 diag tool will command an autobleed. It's $160.
The Foxwell NT630 Elite is another that lists that ability. It's under $200 as well.
The Innova 3160 will do ABS bleed. It's around $290.
The WiFi MDI clones will do this job with a hacked copy of Tech2 Win and a GM PCMCIA linear flash card binary image. My MDI clone cost me $200 but I believe they're around $250 now. Setting up the hacked Tech2 Win is kindof a pain in the neck and lord knows what kind of malware might be in a hacked copy. I would get a dedicated laptop so you're not installing hacked software on your daily driver PC.
One thing to keep in mind is the ABS controller might need to be flashed with the correct settings for your VIN.
An MDI or a Tech2 will give you this ability but you'll need an AC Delco single VIN programming subscription. Aftermarket SAE J2534 interfaces are generally pretty expensive. My $1200 Autel doesn't have that capability. The GM hardware clones are the least expensive J2534 interfaces of the bunch. The Tech2 is a bit of a pain in the neck to setup for J2534 and the MDI is very straightforward.

Your mechanic might or might not be trying to take advantage. Sounds like he's thrashing around and changing parts. I'm not a fan of parts changers. I'd collect my vehicle and find someone else or fix it my darnself.

 

Hi. Did you ever get this figured out? I am in the same situation. No brakes after the fluid leaked out. Replaced front and rear hoses, calipers, pads, and rotors. Bled with an Autel scan tool. Soggy brakes.
Thanks. Hope you respond

 

If you have a soft pedal you have air in the system. The diag tool ABS bleed exercises the ABS motors it doesn't blow fluid out the bleeders.
The GM service manuals call for using a pressure pot bleeder attached to the master cylinder.

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I usually take a chunk of clear hose that fits the bleeder and run it through a hole in the cap & to the bottom of a soda pop bottle with an inch or so of brake fluid to use as a catch can.
1-Bleed out the air from all four corners til you don't see any bubbles at all in the hose attached to the bleeder screw. I usually go around the car... LR, RR, RF, LF. The rear pipes may have fluid in them with the slug of air behind it. The old fluid will usually be nasty and black or very dark. You'll be able to tell right away when you get to the air bubble with fresh new fluid behind it.
2-Once you've pushed the air out through the bleeders run an ABS bleed with your diag tool
3-Finally bleed out the air again. I used to use blue fluid for this stage but the US federal DOT has regulated that out of existence.
If I get air and the pedal doesn't firm up I run the ABS bleed and the four corner air bleed out the bleeder screws again. I've had to go round four cycles to purge all the air out of the system.
I typically run the pot at 12-15PSI even tho the service info calls for 20. Most systems seem to bleed a little better at slightly lower pressures.

You can change over to DOT 4 brake fluid in this brake system. I run DOT4 in everything.
What's the difference?
DOT4 is a glycol based brake fluid just like DOT3. Both are hygroscopic. DOT4 has a significantly higher wet and dry boiling point than DOT3. If you look up the specs you'll find that you can mix DOT3 & DOT4 without problems but it's recommended that you use one or the other. DO NOT use DOT5 fluids.
If you intend to run DOT4 you can buy a new GM master cylinder cap for a Chevy Camaro that fits this master cylinder and says DOT4 on top. It's GM part number 924578250. I have one on my 2005 K2500HD truck and another on my Impala.

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@hatzie

So you need to use the pressure pot and OBD II with ABS Bleed abilities?