Hi there. It may be that you've reached her "threshold" for total sleep, so extending the first nap results in a shorter p.m. nap. If she is sleeping 12 hours at night you are not likely to get 4.5 hours of napping during the day (2 longer naps plus a catnap are more likely for babies sleeping 10-11 hours per night). Between 1-2 hours is a reasonable nap length for babies who are sleeping well at night, as long as they wake pretty happy and seem OK during the day.
Sleeping so well at night, and waking up and "playing" after 45 minutes, leads me to think that she is really ready to extend. Unless you are noticing clear signs of overtiredness (agitation, "wired" behavior, jerky movements--yawns and eye rubbing are pretty normal for most babies and don't always mean overtired) I would aim for at least 2 hours of A times, and try to gently stretch. Most six month olds can handle between 2 and 3 hours, esp after a good night's sleep. (My spirited dd was doing 2 hours at 4 months with good naps.)
Your plan for A times seems good, but if you notice no change in naps with 2.25 hours A time (again, watching for overtiredness) you may want to try for 2.5 hours. Especially important while you're extending--keep the last portion of A times low-key, reading in her room, snuggling in a chair, etc.