The problem with this idea “The Mass is a participation in this one heavenly offering. The risen Christ becomes present on the altar and offers himself to God as a living sacrifice” is that at the time Jesus spoke those words the heavenly offering of himself had not yet taken place so Jesus spoke of what was going to place in the immediate future, “..which is to be” given.
The sacrifice was made and Christ appeared before God on our behalf, the offering was accepted and Christ sat down on his throne. (Heb. 10:12) He doesn’t remain on the altar anymore than an animal sacrifice was left on the altar forever.
“Like the Mass, Christ words at the Last Supper are words of sacrifice,” yet the only place Christ’s sacrifice could be offered was in heaven according to Heb 9:24.
As Heb. 10:18 says, our sins have been forgiven, there is no more offering for sin. Christ is not still impaled or suffering for our sins.
To get around the fact that the last supper was a memorial meal not a sacrifice the “out of time, he was sacrificed before he died” argument is now pressed into service as though there was no order of events in the stream of time.
The one and only altar that Christ sacrifice could be offered on is in heaven and no where does Scripture say he is offered or present in a wafer and wine to be offered on an earthly altar. Quite the contrary.