Help: drain leak in slab under a radiant concrete overlay!

Hi everyone, I hope I can get some general advice to help us decide how best to approach a major drain line repair we're facing. Thank you in advance for taking time to read and if possible, offer feedback and/or suggestions!

Essentially: We discovered a leak in the drain leading from our kitchen sink. We don't yet know exactly where the leak is located. The sink is on an exterior wall at the back of the house. Our home is on a slab, and the leak appears to be below the concrete surface. We also have radiant system retrofitted over the entire first floor: a 2" layer of concrete with PEX tubing above a vapor barrier was installed about 15 years ago by previous homeowner. That system is currently off with no water circulating and we don't have any reason to think there is a problem with the PEX lines. We removed the cabinet floor above the drain and there's no visible moisture on the exposed concrete surface there (which is the top of the radiant heating layer, that was not covered with flooring near the drain entry point). However, if we continuously running water at the sink, within about 15 minutes later wetness becomes visible outside the house along the foundation, within 5-7 feet of where the sink is located. The origin of the wetness is beneath the siding just above the exposed foundation. Inside, throughout the kitchen, the radiant layer is covered by a wood floor. There's no sign of water affecting in the wood planks (e.g. cupping) near the the sink area, so it appears the leak and affected areas are all below the vapor barrier underneath the radiant layer, and within the base slab.

We had a plumber and remediation company look at the site (we already had them out for a hot water tank leak, on the same wall but about 25 feet away on the other side of the kitchen, that occurred just before this issue was observed!).

Their initial recommendation is to remove the cabinets to further inspect the interior wall for water damage and identify any needed remediation. All of that sounds fine.

The big problem is how to approach the drain leak given the presence of the radiant floor heating system. We don't yet know how far into the drain is where the leak originates, and we don't know what path the drain takes through the slab. I assume it connects somewhere to the laundry room on opposite side of the kitchen (where the water tank referenced above resides) before eventually exiting at the front of the house, which would require the drain to go underneath the the entire first floor, from back to front.

The plumber has generally indicated they can use some kind of tool (boroscope?) to try and find the origin of the leak and the direction of the pipe, but they did not sound confident, and our general impression was the only sure way to address the leak is to tear up the concrete, and follow the pipe until the leak is found, then make a repair and put everything back together.

While that makes sense, I'm very concerned about harm being done to the radiant system, since it resides in the same area where the concrete would be removed and I assume there's no way to avoid damage to it during the process!

For what it's worth, we're planning to be in the house at least 5-10 more years, possibly longer.

Questions — repair approaches: Given relative pros/cons, what would be the overall best approach given our situation:

1. Can the radiant system be sufficiently well protected (and or repaired afterwards) to guarantee reliability if we go through the concrete? How confident can we be in any repairs? We would eventually replace the wood floor in our home, but my fear is a slow leak from the radiant system that only manifests a long time after the drain repair is complete, and which causes much bigger problems inside the living area...

2. I don't know if the drain goes through, or under, the slab, but we live near (within 20 feet of) exposed bedrock so assume tunneling under the house may not be an option…?

3. the plumber suggested another possible option to avoid breaking the concrete is to run a new drain line that ties into the sewer elsewhere. I assume this would go underground along the outside of the foundation around the house to the sewer exit point in the front yard? To me this seems like it may be best (lowest risk) option, but could also be costly…? Fyi we're in northeastern U.S. with cold winters.

4. finally, I understand from researching online there is some possibility or re-sleeving the existing drain (depending on diameter and direction/turns) with a narrower pipe, or an epoxy-coated liner, but these seem to be not recommended due to long term reliability concerns…?

5. something else?

Questions — defining the problem:

6. How can we (plumber) best find the source of the leak? they mentioned some kind of tool (boroscope ?) but didn't seem confident about obtaining a result (possibly due to distance?).

7. How can we best determine the direction of the pipe within/under the slab? Could running (a lot) of hot water down the drain and using a thermal camera work?

Thanks for reading, and I would greatly appreciate any feedback or suggestions!

If we learn anything new in the meantime, I'll add in comments below.

B