You can get BIN tinted to your final colour if you want. The base is white though, so colour matches wont be perfect.
It is more expensive than eggshell paint but extremely durable (more so than eggshell), and like water based eggshell it will not yellow. The sheen level is lower than eggshell, very "nearly" looking like matt.
I have used it to paint whole room walls in the past. There are some caveats though. You will not be able to use foam rollers. The alcohol in BIN causes the foam to expand. I once used a foam mini roller, it doubled in length and became very floppy. I now use purdy or wooster non foam mini rollers. It is very thin, so consider using a decent quality mini roller when painting the walls rather than a 9" roller to reduce the risk of runs or excess splatter. It "dries" very quickly. If you don't work quickly you risk ending up with a heavy orange peel finish. You can add isopropyl alcohol to it to ****** the curing process if needed.
Oh and it stinks, the smell is just the alcohol evaporating off. About an hour after you finish, the smell will be gone.
Cleaning up, ignore the advice on the back of the tin to use meths. That simply dilutes it. Household ammonia will actually break the product down, rather than simply diluting it. Ammonia stinks though, so if the roller/brush has become hard, pour some ammonia in to cut up (plastic) milk bottle and leave it (the brush/roller) outside over night. In the morning the ammonia will have evaporated off, and in the bottom of the container you will have "dust" suspended in water, which can safely be poured down the sink.
I am only recommending BIN because you seem to be resigned to using it as the first coat. If you are applying one coat, why not apply a second coat? The alternative is one BIN and two eggshells.
