Maybe it's about the right time to have you post your VIP config from the bigip.conf. It's possible you have other settings applied to the VIP which conflict with a FastL4 profile??? Also it might be helpful to paste the values of the TCP profile you have applied.
Regarding the window size...the behavior you see was bothering me for a long time until it finally clicked in my brain. Yes, the TCP window size always starts at 4380. The trick is to understand whether the LTM is sending or receiving data. When the LTM is sending data, as in this case, there is no need for the LTM to increase its receive window - which is the parameter you refer to in the trace.
When the LTM is receiving large amounts of data and you do a trace, you'll see that the LTM receive window starts out at 4380, and quickly increases to the value of the Receive Window as specified in the TCP profile that is applied.
The LTM is smart - it starts out with a small window size so it does not need to allocate more memory than necessary for the TCP connection. If it needs to adjust the receive window (when it is receiving data), you'll see it go up.