I was having a look to set you a challenge of lunch at the Anchor Inn slip is here:
https://goo.gl/maps/wXHoeGU2KrT2at Starcross (you'd need a spring tide for the slip) then found this website
Exepert - The Exe Estuary User's Guide: Estuary Locations and Guides quite handy for the Exe and if you did make it that way then Topsham which is lovely looks an easier spot to land
On the way from Teignmouth to the Exe I noticed this place
https://goo.gl/maps/oyzLpHVkuex doesn't look like much of note but might be handy, not used it myself. I've launched my laser years ago from Dawlish itself, my cousin assured me it was a legitimate launch spot I think this is it
https://goo.gl/maps/uAsLEEruxMB2 being Dawlish it'll be busy with holiday makers so maybe not ideal
You might find beaches around that way have buoyed areas with channels for powered vehicles to operate swimmers etc (yellow buoys around Ness Beach
https://goo.gl/maps/WdrW215HVKm) Can't see the buoys on Google maps but they were there last year
Going out from The Teign estuary and turning right - use the channel markers to go out from the channel heading left and then swing around right. You could use your sounder to cut across, I've always given it a wide berth as a local friend lost his friend on that headland from a rogue wave, wind/swell/tide state/sea contour all combining factors it seemed. I've never felt in harms way and have seen locals in hard open boats having a mooch about with fishing rods
You might want to try Maidencombe beach
https://goo.gl/maps/hPP4FvKs32v although looking into that I found this
By Laws - Boats and Yachts for Sale Torquay Devon Uk – Dolphin Diving so maybe you need approval first? Nice little beach anyway
On my travels I noticed a few coves that may make a landing possible this might be one
https://goo.gl/maps/jDCVhMz2VQo sorry so vague I need more time off work so I can explore more! After that cove is Watcombe beach and after that is Oddicombe/Babbacombe. The former is likely to have a launch area for powered craft (generally jet skis) you could ring The Cary Arms
https://www.caryarms.co.uk at Babbacombe and ask if they have (or can see) a pontoon out
https://goo.gl/maps/a6GujKpqzZy
You've got Redgate beach which again is unknown for landing but looks possible, Ansteys Cove after that is rocky so not for landing, pretty to look at though. You'll go past Hopes Nose next past Thatchers Rock and could head across the bay to Berry Head/Brixham or stop in Torquay Harbour for a break
River Dart is Dittisham for an easy pub based SIB friendly stop / base for the river
Look forward to hearing if you manage to fill in any of the knowledge gaps above