The person you took your BG4000 to is a personal friend of mine. He is the primary technician for one of our major radio stations in Australia and works on many things from small circuits to radio transmitters. He has done extensive repairs to my BG4002 (DC motor version) and BG6000 (AC motor version) which is not dissimilar in many ways to your BG4000 deck.
Believe me, when he tells you the transformer is blown, it is blown, apparently it is the primary winding, he believes it is due to the voltage selector being set to 110v when in Australia it should be set to 240v - this may have been done by the previous owner of the deck.
The recommendation to abandon the deck is based on a financial assessment of the situation, not an emotional assessment. In this situation, it appears you are somewhat emotionally attached to the unit (as I am to my two Beograms) and are keen to get it working again.
The cheapest solution will be to find a wrecked BG4000 or similar unit (BG6000 AC motor version) or BG4002 (AC motor version) and salvage the transformer, in Australia i've seen people pay up to $400 AUD for wrecked decks. There has been a distinct lack of these Beograms on ebay or classifieds over the last few months so I'm not sure how lucky you will be.
The other option is to investigate getting the transformer repaired by a specialist. You could ask your current technician to remove it and then drop it off yourself to somewhere like Sulzer Dowding and Mills in Laverton, get it rewound and then return it to your current technician to have it refitted.
He can then begin working through any other issues with the deck - believe me there will be some issues as most of these decks require at the minimum; new power supply caps, lubrication of the arm mechanism and associated dampener mechanism, clean of speed change relays and reid switches, new belts, lubrication of the carriage shaft and a general check of arm alignment and tracking weight and sometimes a few bulbs.
Best of luck
Drew