There are a couple posts on the blogosphere about the "best" or "easiest" program to get OWE in, but I'm wondering what the absolute cheapest way to get it is. Assuming you value your time/comfort at zero (so red-eyes in economy are allowed, etc.), what is the absolute cheapest way to get OWE?

Starting from where?

Since I'm not actually planning on doing this, you can start from anywhere.

I'd say a very optimized DONE3 ex-TYO or ex-OSL, but I'm certainly not going to check the various earnings tables for economy flights to see if it could be done cheaper that way. Not a chance in h*#l I'd do that again, I stopped that in my UA days when they stopped crediting 1 mile flown for 1 status mile. These days premium cabins are the way to go when optimized for status earning.

But from what I've learned from this forum, AA is not the program to do it on unless you're already EXP with them. AS, AY, and perhaps QR depending on your flying patterns seem to be the easiest ones, but again that's premium cabin only. I can't be bothered to check the easiest way in economy. Too many OW carriers credit economy at 25% and I have zero desire to attempt that ever again.

Find an unmarried person with BA GGL and make friends with them.
Or cheap regional business class trips.
But it's the age Old question of why are you going for status if the majority of your flights are status runs?

I'm actually interested to hear this too. I easily requalify Gold every year and I'm on track to be ~300 SP short of Diamond. If there was a cheap way to get Diamond I'd consider going for it.

Diamond in what program? I can't think of any offhand that use Gold for Sapphire than Diamond for Emerald.

Sounds like CX

I suspect that taking advantage of the BA holiday double tier points on a number of sale fares could be the cheapest way. The BA holiday scenario imagines that you aren't starting from scratch - otherwise getting to Gold would need a number of resets. The double points offer is also only open via the UK.

A DONE3/4 would be probably GBP3k / USD4500 including taxes even if super optimised.

BA flights to OTP (Bucharest) from London are probably only about GBP500 for 80x2x2 TPs (320TPs/flight), so three of these flights gets you BA Gold (if you're already Bronze/Silver), noting that BA needs a minimum of four BA segments to move up tiers.

BA gold is 1500 TPs.
LHR OTP is 80 TP one way in business.
BA Holiday scenario for 2x TP requires 5+ night package deal originating in UK, so you're going to be paying for more than just flights. T&C also state UK residents only. YMMV

It seems Royal Jordanian has now the easiest/cheapest way to earn OWE, depending on your home base

I would consider it just for the cool looking elite cards!

Do RJ still send plastic member cards? I don't even see a way to add the digital card to Google Wallet.

I recently status matched Air France KLM Flying Blue Platinum to Royal Jordanian Royal Club Gold Sparrow for 149 USD. Since then, I booked a Platinum Hawk segment-run on Iberia-marketed, Iberia Express & Iberia Regional Air Nostrum-operated domestic itineraries in May. Total cost of the segment runs, incl. positioning flights & overnight stays in a hostel (late arrivals & early departures make relatively expensive hotel room stays overkill IMHO) has come to 1.179,26 EUR which will earn me 2 years of RJRCPH/owe. If I had been able to make use of the current Iberia gift cards 10% discount offer, I could have saved me some...