Hiya hun. Aside from the BFing, your DD sounds EXACTLY like my DS was at that age. We had some horrendous EW too so huge (((hugs))) b/c I know how exhausting they are.
My LO is 17.5months now & I have learned some very important lessons about EMW over the last 12 months.
Can I ask what time she usually goes to bed at night?
The biggest thing I can tell you is that offering a nap at 8.30am for 1hr is just compounding the problem. Offering a too long and/or too early morning nap can just encourage EW to continue b/c they are able to catch up on lost night sleep at the morning nap. And its quite likely she may be overtired by the time the PM nap comes around (hence why some days you only get 30mins).
What I would suggest is that you very gradually push the morning nap back later by 5mins every 3 days until it starts no earlier than 9am. This will be very difficult b/c she is waking so early, but trust me things will not get better unless you do it. You could try walking round the house looking out the windows with her in your arms, read her an extra story, just to help her get through the extra time awake. Let her sleep for an hour, then get her up (even if you have to wake her) & carry on with your morning. Do your PM nap as usual.
Once the nap starts at 9am & ends at 10am, then the next step is to shorten it. So every 3 days, push the start time of the nap later so she is going down at 9.05 & getting up at 10am (55mins). Then down for nap 9.10am & up at 10am (50mins). And so on until nap starts at 9.15am for 45mins. As the Am nap gets shorter you might find the PM nap needs to come a wee bit earlier towards 12.30. Hold at this stage for a week or so to see what effect this has on your wakeup time. If she is still waking early keep gradually shortening the AM nap so it is 30mins from 9.30 - 10am. Hopefully her afternoon nap should lengthen to around 2hrs & this should help your wakeup get later.
She is quite likely to get overtired while you do this & you may get some days where she does a naturally short 30min AM nap & PM nap (like today). FWIW if my LO did a short 30 min (OT) nap then I would bring the next nap a bit earlier so she isn't so overtired. And if second nap is 30mins then I would try & get a very short nap in the afternoon, OR offer an early bedtime.
Ooh that's an epic post. But its what I did in your situation & it really did help.
HTH.x