I'm thinking the 358BFG being based on the WSSM will have too much breech thrust, just depends on the pressure it's loaded to, no one offers any short mag chambered Encore barrels for that reason, loaded to pressures lower than 65kpsi it may work ok in a Handi, I've worked with a 300WSM on and SB2 frame which didn't work out, to much action flex with the big .555" case head even at 30-06 velocities. 
If they go to a 1.8" case length, how about a short necked 35 Remington? There wouldn't be much neck, but crimped bullets may work fine, I push the 180gr SSP in my 22" 35 Rem Handi over 2450fps.
Tim
http://stevespages.com/page8d.htmTrajectory for Hornady .358 dia. 180 gr. SP-SSP Interlock at 2450 Feet per Second At an Elevation Angle of: 0 degrees
Ballistic Coefficients of: 0.248   0.248   0.248   0.248   0.248
Velocity Boundaries (Feet per Second) of: 1440   1440   1440   1440
Wind Direction is: 0.0 o'clock and a Wind Velocity of: 0.0 Miles per hour
Wind Components are (Miles per Hour): DownRange: 0.0   Cross Range: 0.0   Vertical: 0.0
Altitude: 0 Feet   Humidity: 70 Percent   Pressure: 29.53 in/Hg
Temperature: 59 F
Data Printed in English Units 
Range   Velocity   Energy   Momentum   Drop   Bullet Path   Wind Drift   Time of Flight
(Yards)   (Ft/Sec)   (Ft/Lbs)   (Lb-Sec)   (inches)   (inches)   (inches)   (Seconds)
0   2450.0   2398.7   1.96   -0.18   0.37   23430.58   0.000000000
50   2280.2   2077.7   1.82   -0.76   1.67   0.0   0.063465324
100   2117.1   1791.0   1.69   -3.19   3.16   0.0   0.131738660
150   1960.8   1536.4   1.57   -7.57   2.71   0.0   0.205364303
200   1811.9   1311.9   1.45   -14.21   0.0   0.0   0.284951608
250   1671.1   1116.0   1.34   -23.5   -5.37   0.0   0.371167756
300   1539.6   947.3   1.23   -35.92   -13.85   0.0   0.464705669