This might not make sense and it doesn't to me either but instead of pushing down have you tried pulling up and over maybe you have to pull up instead of pushing down...just trying to help....it's been so long since I've had a 4spd shifter.
This usually doesn't turn out so well (we've all been there) I sat on top of the transmission, braced one arm around the crossmember/tailshaft housing and gave the shifter a massive "hulk it" slap/smash (hulk angry...hulk smash...) and the shifter slid over into the reverse row.
I dunno what it's problem was, maybe it just likes it rough :D (or maybe it was just jammed) But now reverse does work. The 'force it till it does work' method rarely works to my benefit, I just don't have that kind of luck, but it worked today :D