best adhesive for FR4 to aluminum
This should be able to be "designed" with a reasonable degree of confidence either from theory alone or with a little experimental help.

The key parameters seem to be heatsink temperature, forces involved and adhesive performance with the materials used.

Independent of the adhesive considerations, the LED mounting temperature has a max upper limit set by the LED temperature ratings. As a first approximation, modern lighting class Cree LEDs are rated at 105 degrees C operating. That's hot by conventional electronic standards - you will not usually want to operate equqipment continually much above that unless there is an extremely good reason to, and lower is liable to be wise.

You do not say what wattage LEDs you intend to use, operating periods and duty cycles, or target temperatures or overall size. These combined will control whether it is possible to build your 'bulbs' without means of exterior heat removal. 

A look at the technical data sheets of a few epoxy adhesives show a wide range of temperature specs. Some basic epoxies  60 C max operating) would not work. Others with a 120 C max "maybe" rating will "maybe" work. 
High temperature epoxies withstand temperatures that would rapidly kill LEDs. 

Examples: 


Here is a semi-randomly chosen epoxy technical data sheet (TDS).
BOSTIK EPOXY BOND 5 MINUTE TWO PART ADHESIVE  


They say


  When fully cured, the adhesive can withstand boiling water for short periods of time.Heat resistance rating of 60ºC temperature continuously. 


ie - it would perhaps meet your needs for LEDs guaranteed to be on for short periods (indicator, stop ...) but would fail in applications where temperatures rose to 105+ degrees.


EVO-STIK HARD &amp; FAST TWO PART EPOXY RESIN ADHESIVE STICK. 
Temperature: -40 C to +120 C depending on conditions of use 


MAYBE! 


Resinstech RT323 High Temperature Epoxy Resin System
Operating Temperature: -50 C to 200 C 


Suitable. 


MG Chemicals High Temperature Epoxy
Encapsulating &amp; Potting Compound 832HT
Constant Service Temperature -30 to +225 °C
Max Intermittent Temp.  250 °C


Suitable.



Looking at TDSs for various silicone rubbers would allow comparison, but there seem to be adequate epoxies available.