Did you test using tcp otimized profiles (tcp-wan for the clientside and tcp-lan for the server side on the VIP)?
https://support.f5.com/csp/article/K03553427
(editors note: condensing duplicative questions&answers onto one page)
If you have AAM module then you can convirt GIF to PNG format for example:
https://techdocs.f5.com/kb/en-us/products/big-ip-aam/manuals/product/bigip-acceleration-implementations-13-0-0/15.html
JPEG-XR comperssion is nice for GIF compression as th other compressions may have the reverse effect:
https://techdocs.f5.com/kb/en-us/products/big-ip-aam/manuals/product/aam-concepts-12-1-0/22.html
Nimbostratus
