... AKA the sequel to "Best Android phone options <$400?"

Back late last year I sought some advice re sub-$400 Android phones, as per that link; the phone I ended up getting my wife was a Xiaomi Redmi Note 2, which has generally been good but has an occasional but still fatal flaw that makes it unsuitable for a work phone (which is what she now needs), so I'm back looking.

Generally, I'm after overall better features to last time (given it's intended use as a business phone), and acknowledge the need to lift the budget to get something suitable.

Must haves (the key ones are captured in this Pricespy search):

 

1. $700 or lower (could stretch a little more for something brilliant)
2. screen at least 5”, preferably 5.5" (her current size)
3. work on all networks (rules out Vodafone Ultra, but the recent reports of screen probs would also rule it out)
4. 4G (again, on all networks)
5. has a decent camera
6. minimum of 16GB RAM; 32 or 64 if no SD card slot
7. running at least 5.0
8. be appropriate for and reliable as a business phone

Preferable features:

• SD card slot
• decent screen resolution of at least 1080
• still be supported for the next couple of years in terms of updates (even if not to new Android versions, at least receive patches)

Must not:

• be only available as a Chinese import (a la Xiaomi etc) - not willing again to risk buying something half-baked that the manufacturer shows little interest in putting back in the oven
• have lots of bloatware - I'm not keen on Samsungs, partly on this basis, partly just 'cos for some reason I don't generally like their phones, irrational though this may be

Happy if it's:

• a parallel-imported version of a phone otherwise available here; just needs to be available from a reputable retailer that'll issue a legal NZ tax invoice; would prefer a standard NZ retailer, but realise it's unusual to get a truly decent phone at a good price from such a shop (that said, saw the post where HN's had the G4 for mid-600s).
• an oldie but a goodie (ie, former flagship); would prefer this to a more modern but compromised phone

Appreciate any recommendations on such a phone, and thoughts on the ones thus far identified (as per list below). Thanks!

Possible models identified thus far:

• LG G3 (mid $400s for 32GB D855)
• LG G4 ($600sh up; don't want the leather back)
• HTC One E9+ 32GB (mid $500s)
• Nexus 5x ($600sh for 16GB; $700sh for 32GB)
• Moto X2 ($500sh for 16GB)
• Huawei P8 (mid $600s for 16GB)
• If I must: Samsung S5 ($400s) or S6 (around $700)

At this stage, I'm tilting towards the G3 as it's a known quantity (I've got one) and gives a lot of bang for buck despite its age; alternatively, may look to the (plain-backed) G4, the price of which should drop when the G5's released.

(Edit: edited to sort formatting; numbers used only as bullets wouldn't format correctly.)