@Dan Yes, I concur with all that a machine upgrade may help, as it will allow you (depending upon the machine) to control key variables throughout the shot. And learn their impacts on taste.
You need to be able to control temperature and ideally flow (through pressure), during the pre-infusion, commencement, full flow and tail of the shot. And the time duration of each phase.
A lever machine will allow you to do the above manually, in combination with an accurate scale with timer. An automated machine (like a Lelit Elisabeth) will allow you to control all but flow. A Lelit Bianca adds flow control. My Decent DE1 allows complete control of all.
If you have the budget for a Lelit E, I would strongly recommend that you stretch to buy a Lelit Bianca, to get flow control and generally better machine quality.
Fyi, while well designed, the Lelit E definitely has some parts design flaws, such as its OPV and its steam knob and valve. You get what you pay for.