I don't know of any free sites that are better than the one you've already found, but I do know of this site that I have used before. It does cost money but it works well.

The problem with newspaper from the period you are looking at is that a lot of them is not in public domain yet and can therefore not freely be shared. Here is a guide to when something becomes public domain.

Another problems with these kind of databases is that the technique used called OCR (Optical Character Recognition) is not always reliable. They do often swap letters for one another and therefore don't give you all actual newspapers mentioning this. I have mostly used Danish newspapers, so I don't have any English examples, but I can give you a Danish one. If you search on the Danish site Mediastream for "magtskifte" (change of power), it recognizes words that are not "magtskifte" as that word. One of those words is "majestæt" (majesty) and another is "mageskifte" (I cannot find the correct english translation, as google also confuses these two words).

My point with the paragraph above is that you need a lot of patience because you have to read a lot of newspapers to maybe get a somewhat correct result, and you probably also need to try and search on misspelled versions of what you are looking for.

I do wish you luck with your search and I hope you find what you are looking for!