First, I think there's a mistake in your value of Flory's constant; it should be an order of magnitude smaller. This ref

http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-50532005000300017quotes values of Φ from different theories with a range of 1.81-2.87 x 10

^{23} /mol (misprinted as 10

^{-23}). I haven't been through all the data, but for polybutadiene and polyisoprene I get very good agreement (in those cases where both [η] and R

_{g} values are given), using a value of 2.5 x 10

^{23} /mol, in the theta solvent dioxane. The agreement is less good (particularly for PIP) in the good solvent cyclohexane, and gets worse with increasing molecular weight. (This would not give R

^{2} = 1. Can you share your data?)

I don't know the derivation of your equation - whether, for example, it only strictly applies to theta solutions, in which [η] and R

_{g} both vary as M

^{1/2} - but looking at the fearsome equations in the brazilian ref it seems that significant modifications are needed for good solutions - which may be interpreted as a varying "effective Φ". Your point about second virial coefficient then seems on the right lines; the theta condition [polymer, solvent, temperature] is that at which A

_{2} = 0, the strong interactions in good solvents complicate things.