I don’t see any major problem of using Remote Desktop over a L2TP or IPSEC VPN (knowing that both can be implemented using only Microsoft technology).
As for LogMeIn I also have some reserves once the session traverses devices that you don’t know and don’t have any control over.
I haver several clients with hundreds of L2TP VPN clients that remotely connect to an ISA server. They mostly use Remote Desktop for Terminal Services without any issue for some years now.
Please post back, if you think I can be of further help.