I agree with Ken C's suggestion to get a better (pressure) bleeder -- although the pedal method is OK, per the 240 greenbook brake manual.
Surprise at the Beck-Arnley MC. FCP's listing says "Ate", which is OEM. B-A is just a repackager -- no telling the source.

Since the 200's have two separate hydraulic systems, the recommended sequence (below) bleeds each system separately.

Either A or B can be done first:

System A:
1) Left rear
2) Left front - Upper piston chambers (single bleeder, top)
3) Right front - Upper piston chambers (single bleeder, top)

System B:
4) Right rear
5) Right front - Lower piston chambers (inner and outer bleeders, either first)
6) Left front - Lower piston chambers (inner and outer bleeders, either first)

On the front calipers, the upper two cylinders form an inverted "U", with a single bleeder at the highest point. The lower two cylinders form an upright "U", with bleeders at the two high points. The upper and lower cylinders are each in a separate hydraulic system.
(See illustrations in Bentley, p 500-1 and Haynes, p 9-13)

--
Bruce Young
'93 940-NA (current), 240s (one V8), 140s, 122s, since '63.