ILR means that you have rights to stay in the UK as a resident permamentaly, as you think you want to settle down there, and live there for the rest of your life (or at least for a long time).
However simply leaving the UK, and getting a temporary (less than two years) residence elsewhere is fine (as there can be lots of valid reasons to be outside of the country while still retaining the intent to return to the UK as a permanent resident). But when returning to the UK in that two year period you have to return to the UK with the explicit intent of continuing your residence there (not as a tourist or a visitor), otherwise they will deem that you don't want to be a resident anymore in the UK, and will revoke your ILR status.
Being outside of the country for more than two years is also an indication that you don't want to remain in the UK, and will mean that your status will be revoked.
From what you described, you clearly want to get some kind of EU citizenship, but prefer that to be an Italian one, and you want to have a backup plan, which is fine. There are multiple routes:
Option one for you would be to try to get yourself naturalised as a UK citizen while you are still in the UK. While you won't be an EU citizen this route anymore (as of 1 February 2020) dependent on the UK-EU agreements it might still ease your status in Malta, Italy and any other EU countries.
Dual citizenship (also known as dual nationality) is allowed in the UK. This means you can be a British citizen and also a citizen of other countries.
Note that in order to get naturalised you have to intend to remain in the UK, which you clearly don't want to do, so any plans on moving away should be done after you've got your citizenship.
As from 16 August 1992, Italian citizenship is no longer lost in concomitance with the acquisition of foreign citizenship unless the Italian citizens formally renounces it, and save international agreements.
So you can keep both the UK and IT citizenships, and the IT one will provide you the right of Free Movement inside the UE
Option two is to go to Malta, and if you happen to figure out that you won't be able to get the Italian citizenship then quickly return to the UK with the explicit intent of staying there (you have to state this to the immigration officer).
You have to do this in the two year period after leaving, but preferably as soon as possible. You also have to abstain from entering the UK before returning for any other reason, as they might revoke your ILR in that case.
Note that following this route only means that your ILR status remains intact, but you might still lose right to get naturalised, as for that you have to be in the country for 450 days in the 5 years and for 90 days in the 12 months prior to the application. If you are in Malta for a long time, then it's possible that you'll be out of the 450 day rule, so while you retain your ILR status you might still lose the ability to obtain the citizenship easily (or at least you have to wait a few more years).
Option three is of course to get the Italian citizenship if you can, as an Italian citizen you will also be an EU citizen, and if you move back to the UK before the end of 2020 you can get a pre-settled status allowing you to remain and work in the UK. This won't give you the same benefits as an IRL, and is only viable until the end of 2020 after which there will be different visa requirements for EU citizens in the UK.
Option four is to remain in Malta for 5 years and try to get a citizenship there. Malta is both an EU and a Commonwealth country so getting a citizenship there is also beneficial in both Italy and the UK.
Either option you chose, for tax reasons there is an EU-wide tax treaty, meaning you'll only have to pay the usual taxes in the country where you are actually residing: in this case it will be Malta. You might be liable to US taxes as well however.
