This whole subject is dealt with, admirably and historically, by the Wikipedia article Lord's Supper in Reformed Theology and I thoroughly recommend it.
The word ποιέω in Greek (see Strong 4160 and, therein, Thayer's comments in particular) covers a variety of concepts expressed in English by 'make' 'do' 'fashion' and (notably in this case) 'cause' and 'prepare'.
The word has a very broad spectrum of concept, which can be conveyed (mostly) by the word 'effect' in English : 'cause to occur' or 'effectively cause to be so'.
Therefore 'do' this cannot be forced to mean 'cause a supernatural thing to occur' or 'make a profound alteration to be so'.
In order to understand what part of the very broad spectrum of meaning is (in context) to be attached to ποιέω one must needs observe the following noun phrase 'in the of Me remembrance' (literally, see Biblehub).
... this do in the of Me remembrance [literal Luke 22:19]
ἀνάμνησις, anamnesis - ana/mneia again/mention - (see Mounce) is only used four times in scripture, three times in connection with the remembering of the supper, Luke 22:19, 1 Cor 11:24 and 25, and once (significantly) Hebrews 10:3 :
But in those (sacrifices there) is a remembrance again made of sins every year. [KJV]
The contrast is with the remembering one's own sins, repeatedly.
Instead, Jesus institutes a memorial of his sacrifice.
I am going to repeat that, so needful is it to state it :
Instead of remembering one's own sins repeatedly, Jesus institutes a memorial of his sacrifice.
Hebrews specifically remonstrates against the repetition of a sacrifice, showing how ineffectual such a repetition is, Hebrews 10:2, Hebrews 10:14, Hebrews 10:18.
Instead, there is one sacrifice.
And it is to be remembered - not repeated.
It is a memorial, not a 'sacrament'. It is an 'again mentioning'. What is to be 'effectively caused' is an 'again mentioning'. It is not a repetitive ritual : it is an oft reminder which is 'mentioned'; the emphasis being on intelligent (and shared) communication for mutual benefit. It is a gospel matter not a ritual matter.
The Question by the OP, is a very astute one, noting the wording precisely.
The word ποιέω requires to be defined (due to its exceedingly broad spectrum of meaning) by the context of 'remembrance'.
'Effectively cause (in the context of memory) to be so'.
Thus 'remember Me' rather than 'remember your sins'.
Remember his suffering, remember his sacrifice, remember his obedience to the Father, remember his love to the sheep.
'Effect this in memory of Me'. 'This' being the taking of an ordinary loaf, breaking it open, and distributing it in a simple memorial of an utterly unique occurrence.
The alternative is to repeatedly detract from that unique occurrence by instituting a repetitive occurrence that draws attention to itself, and draws attention away from Christ.
The sacrifice of Christ purges once and purges forever. It does not need to be repeated : only to be remembered :
For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins. Hebrews 10:2 KJV.