The old units are not that sensitive for sure - can you lower your hot water temperature on the tankless unit? If you were able to lower it you can use more hot water at the faucet thus creating the flow that you need to trigger it.
You can also change your aerators to a higher flow rate. WaterSense
just means that you need a flow rate of less than 2.5GPM at the faucet & they need to be pressure compensating to ensure continuous flow. You can get models with 2.0GPM, 1.5GPM, 1.0GPM. The swap out is easy. If you want high quality aerators consider the Neoperl product. You can get them on Amazon or GP Conservation
. It's engineered by the Germans and made in the USA. They cost next to nothing. It is the same stuff that goes in high end faucets. I have swapped the aerators out at my apartment complex. It is really easy. You can do this by hand.
In any case I would recommend trying to reduce the hot water temperature first. If this does not do it go aheead and swap the aerators out for something with slightly higher flow.
What is the use of a tankless gas water heater if you don't get hot water?