I'm replacing a 24 year old Bryant heat pump thermostat with two mercury switches, part number P271-3457 with a Honeywell RTH7400. It controls a heat pump/air conditioner with electric thermal storage (equivalent to electric resistance backup) as second stage heating. The Honeywell manual and website do not cover my situation, as all 8 thermostat wires are connected to the thermostat and there are no jumpers:

Wire Color - Old Thermostat Terminal

Red - R
Org - O
Yel - Y
Grn - G
Brn - C
Blu - E
Wht - W1
Blk - W2

The Honeywell guidance only covers a maximum 7 wires and provides for either W1 or W2 connecting to the AUX terminal, but not these wires going to separate terminals.

Any advice for a frustrated electrical engineer?

Your old thermostat was set up for 3 stage heat. Y stage one, w1 stage two, one bank of electric heat strips and w2 stage three the second bank of electric heat strips. The white or the black will work for the aux heat just cap off the one you don't use. You can also put your black and white wire together to bring on all banks of electric heat in second stage. Warmer supply temp but it cost more to operate.

The wire color axialcompressor mentioned was wrong, I almost burn my transformer.
The correct one is following:

Wire Color - Old Thermostat Terminal
Red - R
Org - O
Yel - Y
Grn - G
Brn - E <<<!!
Blu - C <<<!!
Wht - W1
Blk - W2