Try downloading the driver package from the Surface support site then remove the Marvell WLAN from device manager and reboot. Windows should reload the driver if not unzip the folder of the driver package and load the driver from there....
So just the SP3 Driver set that's in the ppkg file? The only package zip I can decipher is the one they have for SP1. I'm kinda missing the old days here when things were easier to find and with more clear labeling. I do have the ppkg file on the surface now and have rebooted several times after uninstalling with it there.
EDIT - Nothing has changed in doing that. If I get speedtest to connect, it's still the same 0.65 down and 5.65 up.
Said list:
Surface Ethernet Adapter.zip
Surface Firmware Tool.msi
Surface Gigabit Ethernet Adapter.zip
Surface Pro 1 - January 2015.zip
Surface Pro 3 AssetTag.zip
Surface Pro 3 Driver Set.ppkg
Surface Pro 3 KB2978002.zip
Surface3_NAG_Win10_150724_2.msi
Surface3_NAG_Win10_150724_2.zip
Surface3_NAG_Win8x_150724_3.msi
Surface3_NAG_Win8x_150724_3.zip
Surface3_ROW_Win10_150724_3.msi
Surface3_ROW_Win10_150724_3.zip
Surface3_ROW_Win8x_150724_3.msi
Surface3_ROW_Win8x_150724_3.zip
Surface3_US1_Win10_150724_2.msi
Surface3_US1_Win10_150724_2.zip
Surface3_US1_Win8x_150724_3.msi
Surface3_US1_Win8x_150724_3.zip
Surface3_Win10_150723_0.zip
Surface3_Win8x_150623_2.msi
Surface3_Win8x_150623_2.zip
SurfacePro_Win10_150723_0.zip
SurfacePro2_Win10_150818_0.zip
SurfacePro2_Win8x_150519_0.zip
SurfacePro3_150623.msi
SurfacePro3_150623.zip
SurfacePro3_Win10_150818_1.msi
SurfacePro3_Win10_150818_1.zip
Windows8.1-KB2969817-x64.msu
Wintab-1.0.0.18-64-bit.zip