I'll say it again.. 
In real life, the carrier would NEVER even come close enough to be seen.. NEVER!
And yes there was surface search radar in WW2, on ships, and in Aircraft..
Give us separate invasion fleets to park off shore, so the Carrier won't have to
sit there motor boatin back and forth looking stupid.. Partial Fix for the Problem..
For every "C" task force, there would be a corresponding "I" task force from the same port!
PLEASE 
I've been asking for this for a LONG time. In fact, I'd have three task group types:
1) CV Group - Task Group as it currently exists, however remove LVTs and PTs. Restricted to operating no closer than 25 miles of enemy fields.
2) Bombardment Group - Replace CV with a BB. Add float plane scouts (OS2U Kingfisher, F1M "Pete", etc.) and remove all other vehicle/aircraft spawns. Can close halfway between 25 miles and current minimum approach distance.
3) Invasion Group - 1 LST (LVTs/PTs) escorted by 1 CVE with limited plane set (TBM, SBD, F4F, FM-2, Seafire, A6M, B5N, D3A) and a couple DEs. Respawn triggered by loss of LST. Can close within the current range of shore as current CV groups.