Moving a 5,000 vinyl LP collection safely

I recently moved from the lower Hudson Valley to Austin, TX, with approximately the same number of LPs. I packed them myself in double walled boxes that I got in bulk from one of the specialty suppliers, Bags Unlimited. I numbered each box and had a word document (i'm not great with spreadsheets) inventorying them, some specifically by title, others by catalog (where I owned a lot of a particular catalog). The movers taped the boxes, and hauled them from a third floor to the truck.
This was in the dead of winter, so heat wasn't the issue, but water slop was. The records were taken to storage in Conn. and in mid-April, hauled to Texas. I don't think 80 degree F temperatures are a big deal.
 Since commercial movers are what they are, no matter whether "white glove" or not, it may be worth talking to your insurance broker for some additional insurance during the period the records are in the mover's hands. Not that this is a complete solution, but it may give some additional comfort. 
My records arrived unscathed. 
Hudson Valley is beautiful in autumn and spring. Sounds like you are going north of Bear Mountain, which is approximately 50 miles north of the city. We were near Piermont. 
Good luck, time consuming, tiring but you'll get it done. 

There's a section of Newburgh near the river that is old houses+ gorgeous. I forget what it is called. Yeah, it is a little rough there. I used to drive my sports cars and bikes north and would sometimes come through in one direction or another. 
And agreed, before it was called Noho, that area between the Village and Soho wasn't exactly grandma friendly. We lived in Brooklyn long before it was 'chic' and there were some very "edgy" neighborhoods as well. Now, it is unicorns and 20 dollar cocktails.

The Hudson Valley can be spectacular. Lot's to explore. Good luck w/your move. 

Congrats on your new home. I don't envy you the process of a gut renovation of an old townhouse, but if you can deal with it in liveable stages, i'm sure you'll have a great place to live when you are done. We found that living in a place for a while gave you a better sense of what demolition and reconstruction made sense--been through it myself, but never did an entire house. Good luck and enjoy.