Can I pray with a Muslim if we're addressing our prayers to a common Creator?
Well of course you can. The question is whether you should. And I think that it's not helpful, by and large, either personally or at some ecumenical gathering, to do that without clarifying the differences.
In other words, you can pray with anybody at any time, but if the praying creates the impression that you're all going through the same mediator in the same way to the same deity, understood in the same way, you're lying! And you shouldn't! It's very unhelpful and misleading to people not to make clear that you're going to pray in Jesus' name.
I'll give you an example. For 10 or 15 years I belonged to a clergy group that was all over the map, including Jewish. So it included liberal protestants, a few of us evangelicals (two, maybe), and Jewish. It was really awkward to know what to do with this fellowship. "Fellowship" would be an unhelpful description of this.
One day I was asked to pray. It was usually a breakfast meeting, and I noticed how they had been praying: they never prayed in Jesus' name. And so I did pray in Jesus' name. I didn't say, "In Jesus' name we pray," because there was the rabbi sitting three people over, and he wasn't praying in Jesus' name. So I said, "In Jesus' name I pray, Amen."
He was very offended. He told me later, "I'm very offended you prayed in Jesus' name." I said, "Well look, it's not right for you to dictate the way you pray on me, that I have to pray that way!" The assumption was that we're all able to use "God" and leave Jesus out, but that's not true! I can only get to God through Jesus, and I want to make that clear to them. And I'm not putting that to them. They don't have to pray in Jesus' name when I say "I."
So I think it's good at ecumenical gatherings and personal smaller gatherings just to look a Muslim right in the eye and say, "Let's just clarify for each other how we understand God. I believe God is the Father of our Lord Jesus Christ. He's the triune God: Father, Son and Holy Spirit, equal in persons. The Son has come into the world to die for our sins. The only reason I have any reason as a sinner to go into the presence of God and ask for anything or praise him is because of the blood of Christ covering my sins. So when I go to God, I say 'In Jesus' name' to signify that my Mediator is my only hope of connecting with God.
"I know you don't see it that way. I just want you to know, that's the way that I can only come to God. So when I pray, I will be praying that way, I will be understanding it that way, and I'll be using the name of Jesus that way. And I know you won't.
"If you want to pray in the same room with me, that's OK. I'll pray for you, that you will love Jesus. And I suppose you'll pray for me, that I will see Mohammed as the true prophet and Jesus as a prophet like him, but not more."
As long as you're clear, you can do anything with anybody, almost. (That's an overstatement.)