This is something your feeder could handle...
A 6AWG aluminum feeder landed on 75°C lugs (such as those found in loadcenters and on circuit breakers) can handle 50A. If we apply the Table 220.55 calculations, starting with Note 4:
- Branch-Circuit Load. It shall be permissible to calculate the branch-circuit load for one range in accordance with Table 220.55. The branch-circuit
load for one wall-mounted oven or one counter-mounted cooking unit shall be the nameplate rating of the appliance. The branch-circuit load for a
counter-mounted cooking unit and not more than two wall-mounted ovens, all supplied from a single branch circuit and located in the same room,
shall be calculated by adding the nameplate rating of the individual appliances and treating this total as equivalent to one range.
, we get an equivalent range nameplate load of 20.4kW for your new cooking setup, considering that the microwave's 3.4kW is included in the oven's overall 9.6kW load. We then apply the process from Note 1:
- Over 12 kW through 27 kW ranges all of same rating. For ranges individually rated more than 12 kW but not more than 27 kW, the maximum
demand in Column C shall be increased 5 percent for each additional kilowatt of rating or major fraction thereof by which the rating of individual ranges exceeds 12 kW
, which yields a 45% increase (5% * 9) over the 8kW baseline value from Column C for a single range not over 12kW, or a factored load of 11.6kW. Dividing this by 240V yields just over 48A, which is just under the 50A your feeder is rated for.
But, you'll have to do something with it anyway
The other issue with your feeder is that it's a type SE style U cable, with only 3 wires (2 hots and a bare ground/neutral). This is no longer usable for a 120/240V circuit in new work, as neutral and ground must be separated now as per 250.24(A)(5):
(5) Load-Side Grounding Connections. A grounded conductor shall not be connected to normally non–current-carrying
metal parts of equipment, to equipment grounding conductor(s), or be reconnected to ground on the load side of the
service disconnecting means except as otherwise permitted in
Note that you cannot apply 250.32(B)(1) Exception 1 in this case as the subpanel is in the same structure, nor can you apply the rules from the exception to 250.140, even if the subpanel was removed, due to having to replace the ungrounded 10/3 NM cable, as described below.
However, what you can do is remove the bonding screw in the subpanel, add an Eaton GBK5 ground bar to the subpanel, and run a bare or green 10AWG ground wire from the subpanel to the main panel by any route you can find, connecting it to the ground bar in the main panel; if you can't get to the main panel, then running it to the nearest grounding electrode conductor and connecting it using a mechanical T-tap (Ilsco GTT-2-2 or equivalent) works as well. This is within the spirit of NEC 250.140(C) (and its letter if you remove the subpanel's interior, even).
The 10/3 NM will have to go as well
The existing 10/3 NM cables will have to go the way of the dodo as well, as they are undersized for the new loads you are placing on them (10.8kW aka 45A for the cooktop circuit and 9.6kW aka exactly 40A for the oven circuit).
The good news is that since the overall circuit is 50A, we can apply the provisions from 210.19(A)(3) Exception 1 here, which means we don't need the subpanel. However, that doesn't get us much in terms of downsizing the wire since the cooktop requires 6AWG wire anyway.
(3) Household Ranges and Cooking Appliances. Branch-circuit conductors supplying household ranges, wall-mounted
ovens, counter-mounted cooking units, and other household
cooking appliances shall have an ampacity not less than the
rating of the branch circuit and not less than the maximum
load to be served. For ranges of 8¾kW or more rating, the
minimum branch-circuit rating shall be 40 amperes.
Exception No. 1: Conductors tapped from a 50-ampere branch circuit
supplying electric ranges, wall-mounted electric ovens, and counter-mounted electric cooking units shall have an ampacity of not less than
20 amperes and shall be sufficient for the load to be served. These tap
conductors include any conductors that are a part of the leads supplied
with the appliance that are smaller than the branch-circuit conductors.
The taps shall not be longer than necessary for servicing the appliance.
Given all this
I would get a spool of 6/3 W/G NM-B, sufficient to replace all of the wiring involved in this setup. If you want to retain the subpanel, that's fine albeit not necessary; you'll want two CH250 breakers if you're retaining the subpanel, as well as the CH250 you'll need for your main panel in any case. You may wish to let the electrician do the runs, especially for replacing the feeder back to the main panel, though.