Setting "Is the first amount and period different"
to
"Different first period and price for Registration only"
will still bring up
"one year for -> then" in upgrade.

Since it is explicitly stated that the above setting applies only to Registration, I believe it shouldn't appear in the upgrade plan proccess.
When upgrade is clicked, the first period amount is not calculated in price, so in practice it is inactive but very confusing for the user who would expect the price shown on plan for the first period.

Case 1

Original price = 100 / yes first period = 30 (set to Registration only)
Plan option 6m = 50 / no first period
Plan option 3m = 25 / no first period

Outcome = first period value (30) appears in upgrade ("one year for -> then")

Case 2

Original price = 100 / yes first period = 30 (set to Registration only)
Plan option 6m = 50 / yes first period = 10 (set to Registration only)
Plan option 3m = 25 / yes first period = 5 (set to Registration only)

Outcome = first period value appears in all price options in upgrade ("one year for -> then")

Doesn't make any difference. First option does appear in upgrade

Does it still show when actually in the basket after selecting an option that has no first period price?

I have mentioned this above "...When upgrade is clicked, the first period amount is not calculated in price, so in practice it is inactive but very confusing for the user who would expect the price shown on plan for the first period." ( price-for-initial-period-issue#330121 )

EDIT: Reading again your question,
when in basket:
1. Original price doesn't show first period, just the original price since "Registration only" is set to original price first period. ( it works ok)
2. Price options doesn't show first period just whatever price set to 6m, 3m, etc. since "Registration only" is set to price options. ( it works ok)

when in upgrade (before basket):
1. Original price shows first period although original price has first period but is set to "Registration only". (doesn't work properly here)
2. Price options show first period although prices have first period but is set to "Registation only". (doesn't work properly here)

So what actually happens is that the user expects different price for the initial period since this is what the plan shows although it shouldn't. I suppose it is an

"...override problem..."

as you mention but IMHO a bit serious one as a user could perceive it as a misleading procedure especially because money is involved.