When it comes to your wedding invitations you will always want them to look there best no matter, but there are just some things that you will need help on. The only things I would recommend changing are as follows: removing the comma after Street in the reception location address, and moving "Saint Paul, Minnesota" down to the next line.
In terms of the "together with their parents" line, placement depends upon who the hosts of the reception are; generally (and this is regardless of financial contribution), the hosts of the party are the parents of the bride, or the parents of the couple. The hosts always receive top billing on the invitation, as they are the people technically issuing the invitation. For that reason, I generally advise that "Together with their parents" appears at the top of reception-only invitations.
When writing the invitations, just mention the ceremony. Make no mention of a reception and most people will understand that they are just being invited to a ceremony.
I would have a friend -- best man, maid of honor, somebody send out a separate card that is more casual that includes the other information. Gift information is not appropriate in any way coming from the two of you -- and the Dutch info might more efficiently be expressed by someone writing on your behalf. That way you guys can focus on sending out an invite with standard wording and not have to worry about the other details.
By all means send them an invitation too. As a matter of fact I was asked a question by a guest that received a save the date card and did not receive an invitation when they thought they should have. A save the date card is just saying get ready and plan for it. The invitation is telling them to come.
The best way to make your wishes known is via word of mouth. For the invitations, do not put any information about the reception at all. Instead tell your bridal party and family what you wish to do and have them pass the word along to guests. While they're telling the guests about the Dutch dinner afterward (don't call it a reception at all or guests will think that you are paying), they can also inform the guest (but only if the guest asks) that you would prefer to have gift cards as you are moving. Keep in mind that some people will still insist on giving a physical gift. Perhaps make arrangements to have your family in the states send a shipment to you after you are settled.
There is a widely-held assumption that if a person's parents are listed by name on the invitation, it has something to do with finances. In terms of etiquette, this is a common misconception which often does nothing but create a source of anxiety for brides, grooms and their families.
Traditional invitation etiquette demands that there is *no indication* of who is paying for what in the wording of the invitation. In fact, the reason that only the bride's parents appear on traditional Christian invitations has to do with the idea that the bride's family is "giving her away," with their blessings, into marriage to the groom. The groom is assumed to be a man with the means to care for their daughter, without his family's assistance.
In Jewish tradition, both parents are mentioned, which implies that both families are supportive of the impending marriage in spirit, rather than financially.
In your situation, I would suggest choosing the wording that you and the groom-to-be feel best represents your wedding: very formal and traditional, casual and contemporary, or somewhere in between and simply goes with that.