It sounds like you may be reacting a bit too hastily to the Libre arrows. Are you aware that there is a time lag of 10-15 mins between what the Libre shows and what your BG is doing?
As regards the spikes after food and then rapid drops, pre bolussing really is key. Find time, on a weekend perhaps, when there are less work pressures, to experiment with injecting that breakfast insulin earlier.
To put it into context, I need to inject my NovoRapid as much as an hour before eating on a morning to prevent a huge spike but I only need 20 mins at lunchtime or in the evening. Also, even if I am not having any carbs (ie an omelette), I still need to inject 1.5-2 units of bolus insulin to cover Dawn Phenomenon. There are other members here who find the same but probably many people who would hypo waiting so long before eating. That is why experimenting by increasing the time between injecting and eating by 5 mins each day will help you find the "sweet spot" for you where the insulin starts working as the carbs hit your system. Having the LIbre is a huge benefit with this testing. I usually wait until my Libre shows a downward arrow in the 5s before I start eating. It will continue to drop after eating and level out in the low 4s or high 3s and then start to rise but I usually find the Libre reading is a bit lower than my finger prick BG particularly at the lower end of the scale so I don't worry if I drop into the high 3s as I rapidly come back up with the food that is starting to digest in my system and DAFNE guidance actually considers a hypo as 3.5 or below rather than the standard 4.
Timing of that injection does also vary a bit if you are starting the day low or high as you have realised, so if you are high it will often take longer for the insulin to have an impact whereas if you are low it will usually take less time and as
@Kaylz says, dialling it back by half a unit is usually a good idea (if you have a half unit pen and if not, ask for one) Having that extra flexibility to fine tune the dose by half a unit is a great option.
I also agree that asking for a more modern bolus insulin might be helpful. It definitely sounds like you need a diabetes clinic appointment to upgrade your management and ideally something like a DAFNE (Dose Adjustment For Normal Eating) Course or whatever your local equivalent it. It is an intensive course but hugely beneficial. Unfortunately, with Covid, things are all on hold at the moment both with outpatient appointments and courses but I believe they are setting up virtual courses.
