I can help a bit, as we use either our Alaska miles or our BA Avios to fly to Europe at least once a year.
BA and Heathrow are having their problems right now, but so are most airlines, and other European airports as well (Paris, Berlin, and Amsterdam that I have seen). These issues are mainly caused by pandemic-related staffing problems, and hopefully will be resolved by next summer. But there are no guarantees.
If you want to avoid Heathrow, then your choices with Alaska miles are Icelandic, Aer Lingus, and possibly Condor (they fly direct to Frankfurt from Seattle but have not released flights past April of 2023 so far.). You may very occasionally see American Airlines flights through another U.S. airport like JKF, with a flight from Seattle to JFK on Alaska. But AA’s Saver flights to Europe rarely make it to their partners; they get snapped up right away when they are released to AA mileage program members.
Aer Lingus charges an excessive amount of miles—-60K to fly in Economy each way, so two people would need 240K miles to fly roundtrip. For those same miles, you could fly Business class on BA. Yes, you will pay their very high supplemental fees ( not all taxes) to BA, but we are willing to do that to fly in business class. It basically costs us the same as we would pay for an economy ticket, without the miles.
So Icelandic may be your best option for avoiding Heathrow at this point. Their economy tickets for next June ( as far out as one can book right now) are $35K miles plus $184 miles each way. We have never flown them so I don’t know what their seating fees and baggage policies are. I do not see any business class tickets available on Icelandic.
Award seats from most partners are released to Alaska Airlines 330 days in advance, and you will have the widest range of options if you book them right away. Thus award seats for, say, July 15 2023 should be available to Alaska miles members around August 25. You can book one way at a time to take advantage of this; we always do it that way for maximum flexibility.
A really nice feature of the award tickets is that they can be canceled without penalty if you want to make a change. At least there is no penalty or change fee for the Alaska miles tickets at this time ( perhaps they will re-instate the change fee at some point in the future). It is a simple matter to cancel online; the miles are returned almost instantly so you can use them to book something else.
Watch out for the dreaded “mixed cabin” which is a bad feature of the Alaska miles booking system. It is not a problem if you are flying Economy at all. But if you are looking at Premium Economy or Business class, you may see a little seat icon next to the price, in two shades of blue. This means that one leg of the journey is in business class and the other, generally the long-haul flight, is in economy. But you are charged the full Business class fare in miles and fees. I saw an Aer Lingus flight in the Business Class column for 280K miles. Opening the mixed cabin icon, I found that the flight from Seattle to Dublin was in Economy, and only the short flight from Dublin to Rome was in Business.