I had the same problem with the Q-jet on my 68 GP.
As you know, the tiny fuel bowl on these carbs is known for supply and evaporation problems. Having tried the heat shield also, I installed a Carter pusher fuel pump inline near the tank and wired it to a momentary pushbutton below the dash. A few seconds of priming now result in quick starts, after setting the choke and stroking the carb once. 
Les
66 GTO Sport Coupe,455/trips,700r/2500stall,12bolt/3.08,1.79/13.01/104.5
68 GP daily driver and 2004 Route 66 Tour participant under restoration
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Better lucky than good
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Les Iden
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'65 Buick Sport Wagon Custom, 340, T350, 3:23
'66 GTO Post/468, 700R4, 3.31 (Mike's as of 9-16)
'68 Grand Prix/455, dual AFBs, T400, 2:93 posi (sold)
'72 TA tribute/461, T400, 3.08, (Russ's as of 9-16)
'97 Mitsubishi Eclipse Spyder Turbo, Konis, 5 speed
'09 Torrent GXP, nav, Sun & Sound pkg., Bilsteins
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