Beam A is presumably supporting the ridge beam over a window? If so, the 127 x 75 is OK.
The other end of the ridge against the gable is to be supported on a steel post? If there is a loadbearing wall directly beneath the post, then fine. If not, it is easier to support the ridge off a 1m length of 100x100 box section with welded lugs on it bolted to the wall.
But for the ridge beam, the figures on the sheet are of course OK, but the spreadsheet does not 'tell' the SE what beam to use - it merely clarifies whether or not the beam chosen by the SE will satisfy all the parameters, which it will.
But you could check a massive 1m-deep girder on the spreadsheet and it will still say it is OK; it won't tell you that it's 'too big'.
The skill is in choosing the smallest practicable section, and as above there are a number of lighter, cheaper and more practical sections.
If you have a lighter beam, you might avoid having to use a crane, or alternatively you could have the beam in 2 sections to be bolted together, though there are fab. costs with that.
Maybe have another word with your SE?