HRM and a basic cycle computer will give you a very good and cost effective base for training on a turbo. HRM’s have some lag so actual effort etc will not immediately show but they are still great tools. The HRM will give you an indication of input, Avg HR, then you have time and distance, output. Set your chosen HR zone and then off you go. Warmup and then reset the trip. Say in 30 mins you have travelled 13km before you then cool down. Repeat the same and you should see that for the same time and avg HR you will travel further. This shows your improvement. The turbo will give you the consistency that you will not get on the road/trail. The resistance will be the same each time which you will not get outside. Just be sure that the tyre pressure does not drift.
Training is about getting further for same effort or less effort to get the same distance.
I am not sure what trying to get to a higher HR is meant to achieve.