since we have sent/sent

Either would be suitable tant. there is no difference in meaning.

"since we sent any form of" is most correct in this context.
"have" seems to indicate some form of ownership which i dont believe is necessary in this context.

When we used the present perfect for continuation, eg.

How long have you lived in Singapore?,

we pretty much have to use the present perfect rather than the simple past,

How long did you live in Singapore?

because the latter expresses that the living in Singapore has ended.

In this example, we could easily have two uses of the present perfect; one,

have sent - present perfect of current importance

plus, with the use of,

It has been quite a while

we have that sense of a continued chunk of time which is up to now.

I think that the inclination would be to use the present perfect but that doesn't mean that it would have to be used. The long and the short of it, there's no difference in meaning, there's a difference in nuance, there could be a difference in emphasis.

This is the auxiliary 'have', DadP, not the 'have' of "I have a dog".