I feel like this would work better if Russia had already conquered Ukraine up to and including Odesa.
Russia cannot move forces through Ukraine. That's a hot war, and Ukraine will shoot at them.
I don't think that Russia can fly through Romanian airspace, even with civilian flights, as the EU closed their airspace.
Maybe Russia could fly forces and military cargo into Transnistria in on another country's civilian aircraft. I don't know how much control Moldova has over Transnistria's airports.
EDIT: Apparently the transit issue already came up. Transnistria apparently has three airports:
Until 1989, it was used as a military airfield of the Soviet Air Forces. In 1991, work began on converting the airfield into a commercial airport, which would be the largest in Transnistria. These works were suspended due to the lack of funding and the political unsettledness of the status of Transnistria, which did not allow the customs and border services of the Republic of Moldova to be located at the airport and, consequently, to fly outside the country.
On May 10, 2016, Transnistrian President Shevchuk confirmed the intention to transform the Tiraspol airfield into a civilian airport, but indicated that "neither Moldova nor Ukraine are ready to give the appropriate permissions to transit through their territory or turn around through their territory."[10]
So, basically, it sounds like Ukraine or Moldova need to be onboard for civilian flights to be flying through. They already said no, and even if they did, Moldovan customs officers would get to be at the airport and control (which apparently Transnistria refused).