Hello and welcome zoeblogrow,

There are some solid full gold reps out there, Joshua has a few on his site and is one of the trusted dealers here, have a look at http://www.pc80108.com and see what you can find. Haven't seen any TT with solid center links though but you could get a rep and then fit a gen bracelet to it.

Here's an example of a solid gold rep, it's a day-date rather than a datejust but the cost is $4.288 though which is more than I'd ever risk on a rep purchase.

RLDDF10101 18K President FG Stick Markers Swiss Eta 2836-2
Model : Solid 18K Yellow Gold, Gold Dial , Stick Markers on Solid 18K Presidential Bracelet, Solid 18K Rose Gold Clasp
Movement: Swiss Eta 2836-2 Automatic Movement ( Ceramic Movement Retainer)
Functions: Hours, Minutes, Seconds, Day and Date ( Set via Crown)
Dimensions : Dia 38mm x 11.5mm Thk
Material : 1 piece forged case construction ( 1 : 1 Dimensions ) , Solid 18K Yellow Gold
Back : Solid case back in Solid 18K Yellow Gold
Crown : One-piece screw down crown with o ring
Crystal: Sapphire crystal
Waterproof to 40m
All correct markings
Gold day and date wheel.. Close 6 and 9

Value Added
Waterproofing : Additional seals are add on and watch is pressure tested to 4 to 5 bars... 40m waterproofing guarantteed..

Movement is completely overhaul, oil cleansed.. re-assembled, serviced and re-lub with 5 different types of Swiss imported movement lubricant, Calibration to +5 secs per day.

Above scope of works is carry out by Swiss trained Technicians.

Notes : Mode of payment .. Only Western Union Money Transfer Only.