Mapping – Specify the base units to use in UnitConvert

I'm trying to turn any units into CGS. I know that this can get a bit tricky with ESU, but this question need not be addressed.

I would like to specify an amount to be converted and a list of quantities to convert the quantity. I want to convert a lot into a linear combination of other sizes. This would make the CGS conversion easy, so I could do it.

UnitConvert[Quantity[1,"Watts"]/Amount[2,"meters"], {cm, g, K, s, etc.}]*
Out: ½ g cm / s ^ 3

tl; How do I express a variable as a linear combination of other quantities?

* This is not what UnitConvert actually does, it will overflow the last one.

Relevant sources:

https://mathematica.stackexchange.com/a/101483/45153

Implement CGS unit system in Mathematica 9