Stuck between two frame sizes

I would really recommend that you sort out what you're doing with your bars first. I'm the same height with slightly shorter legs. My road bike is a 56 cm frame with an 120mm stem, my MTB is a 64cm frame with an 80mm stem (and I'd go a bit shorter if I was even sporadically riding more technical terrain). So you're going to get a funky handling bike if you're going to try to switch between flats and drops. 

Don't get a frame that's too big. I speak from experience!

I was buying a Arkose from Evans and on paper I was a large at 5'11".  I had to order a large and when it came riding it, it was way too big. 

Got to agree with the making a smaller bike bigger is the best option and go for the size down.  Sounds tricky in your situation as you can't have a proper test ride!

Large. (As far as I am concerned, no questions.) I'd recommend a 120 stem rather than a 130. 165mm (including 20mm of cups) for headtube not overly short for a racing bike. I wouldn't recommend allowing a delay in availability push you to purchase a bike that's too big for you.

judged by the top tube, I'd pick the 57cm one, (I'm 2cm-s taller than you&have longer legs and arms). 

57cm with 130mm stem.

But the headtube looks very short, even with cups (20-25mm) added. Not really sure what type of frame is this, though from the short chainstays, I guess it's some road frame with sloped top tube& kinda short headtube..

I'd pick the 57cm one if I were you

I'm 5ft 11, i ride a 62cm traditional diamond frame amongst others, my carbon bikes are a 60cm and a 61cm but my commuter/utility ride is a 55cm flat bar but with a long stem with an acute angle, unless you're after a really aero/low down position go with the larger frame.

As the old saying goes, you can make a small bike fit by adding overtly long controls, stems with an upangle like an erect penis and a shit ton of spacers, have half a mile of seatpost sticking out and look like you're riding a kiddies bike but at least it'll work...lol

Tricky one.... but as an example.... I have a customer who is 6'3 and has a similar sceanrio..... he fits a 57 & a 60 cm frame...but not sure which one.... so... 

I'm going to run him out on the road on Tuesday for a 13 mile loop ride.... and swap bikes as many times as we needs....so he can ride both.... then choose the size he prefers.....

but as the old saying goes.... you can make a small bike bigger...but not a large bike smaller...  

For this chap, who even fits a 54 frame with a 120mm stem... I think the 57 will do it for him....