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here is generic upgrade project that has little to NO production downtime

when we do upgrades, we do it  on a copy of production and when ready we replace production with new copy and import out of sync customers/orders..there may be more depending on your shop....

=== checklist .doc'ing

1. identify all 3rd party modules and obtain their 1.7 compatible zips
2. identify core changes (mentioned above), you should also identify template changes (.tpl's).
3. .doc existing overrides
4. select new feature rich theme, we like Leo themes but there are lots of others
5. review existing hosting, most age just like your shop.  it's best to get new hosting account and move to that rather than try to have old hosting upgraded

===  pre upgrade

1. build a test copy of your production shop, then back this up so you can refresh your test system until upgrade completes.  hopefully your hosting allows php level by domain/subdomain so you start out with php7.2.  if not  find new hosting.  
2. uninstall 3rd party modules
3. make sure overrides clean
4. up php max execution time to 'large', 600 or 1200...

===  upgrade

1. back up this test system so you can restore if upgrade fails so you do not have to uninstall moudule/override again
2. perform upgrade 
3. install/configure modules
4. apply core changes
5. install configure theme

===shake and bake until prod ready

== Production installation

1. create a new copy of production to be used for historical purposes
2. import customers/orders from old shop to new shop
3. copy new shop to production or if new hosting (recommended) switch dns 

happy upgrading

el