It's time to share some names...

[Arimeh]

I love Addison - but I'm biased - Addisyn is one of Miss M's middle names

I like Soraya

And I like Hamish Matthew for a boy out of your list

[LimeSlice]

Oliver Matthew
Hamish Matthew

and

Soraya Elsie
Addison Elsie

Great shortlist!!

[Von]

Love Addison Elsie for a girl and Hamish Matthew for a boy

[smiles4u]

Lylah Elsie ... and Oliver Matthew (I like Ash as a middle name but not sure about it with Oliver )

[luna moth]

I like Oliver Ash and Isaac Matthew.
I love Soraya Elsie. Like Addison, but not convinced of Addison Elsie.

[ubba82]

Lexi (Lexie) is my middle name and I really like it! It is actually on our list as a first name! I think Lexi Elsie sounds ok whether you use it together or not. You could swap the letters around and have Lexi Elise (maybe.....)
I like Oliver Ash for a boy.

[JellyBean]

I like all your boy names & middle names! So that doesn't make it easy...
I do however think that Joshua sounds better followed with Matthew, as Joshua Ash is a bit of a mouthful when you say it together- the sh followed by another sh.
I also think that Hamish needs to be with Matthew - as Hamish Ash is too much sh..sh sounding.
Oliver Ash sounds cool - and actually, Issac flows better with Matthew too - the 'ac' sound followed by 'Ash' is kinda similar.
Having said all that, the middle name is only something that will appear on legal documents etc, and you are unlikely to hear them said aloud together very often - so if you like something - who really cares??? I'm just being really picky to help you out!!!

Now for girls..... my 3 faves are Soraya, Jazlyn & Lylah.
I personally don't like Addison (reminds me of Maths ), Isobel is nice but SO common right now, and Lexi is cutesy but more of a nickname IMO. Plus I agree it doesn't go with Elsie very well.
Soraya is likely the most unique and I think very feminine and soft sounding - prob my 1st choice there. What about Siraya? I like that spelling even better.....

Goodluck deciding!

XX