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To get the equivalent 8.4V you could use a 12.6V transformer and a series diode (no filter cap) with the CRT heater. The heater will heat up the same with 8.4VAC or DC.
Or you could rectify 6.3VAC with a filter cap to get 8,4VDC to run the CRT heater.
You might be able to use a CRT brightner in "parallel" mode. These used small transformers to produce around 8VAC from 6.3VAC. In the series string you have, the transformer may make the CRT heater at 8.4V@450ma look like a load of 6.3VAC@600ma.
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