I can prove that the boxes have an effect on the price but not inserts. I have a spreadsheet of the first 40 full of prices with box’s verses no-box. There is definitely a noticeable difference. On some of the more collectables you can see up to a hundred dollars difference, in some cases even more. A Canadian Southern Bell can demand twice as much if it has its castle studios box. Haven’t really followed any of the lighthouses with out inserts. But I would think that the more complete the lighthouse the better chance of selling it for what you want. In other words, it should be worth more.
There are collectors that want complete lighthouse with all its fixings. I know, for I am one. I would never buy a lighthouse without its styrene insert. Unless it was extremely cheap and I would use it for the office.
On the other hand if you have no plan of selling or moving and the only solution you can make-work is get rid of inserts, well so be it. Most likely if it has a styrene insert, its secondary market is only around $35 to$55 anyway and I couldn’t imagine the missing styrene effecting its market price for more than $5.
There are a few lighthouses that have styrene inserts that do demand a secondary market and if all possible I recommend that their inserts be saved. They are of course:

1.All reunion L.E’s and mini’s
2.Big Bay Christmas-The later ones had inserts
3.Grays harbor –rotated top
4.All gold plated event pieces
5.Early Christmas pieces
6.Cape Canaveral


Also you may want to keep styrene inserts for the more intricate lighthouses that have breakable parts.