Word Counter Max for Google Docs is a totally free add-on that I wrote to display the live word count of the current document even for lengthy documents of 5000 words or more. Unlike the default word counter, you will be able to set exclusions to ignore certain text and you can generate detailed reports for your document. There's more, whether you need to hit a minimum word count or reduce your word count to be within the limit for your assignment, you can set targets for that. This word counter should be relatively accurate though there may be slight discrepancies since every word counter considers what should be a word differently. Do write in if there are major errors or bugs.

Available exclusions
▪︎Text between parenthesis
▪︎Text between brackets
▪︎Text in tables
▪︎Text with paragraph styles
eg. "Title",  "Subtitle", "Header1",  "Header2", etc
▪︎Text in paragraphs starting with x.x eg. "1.2 Introduction into" or "1.5.3 My header"
▪︎Everything after and including the paragraph starting with Keyword
▪︎Text in paragraphs starting with Keyword
eg. "Content Page",  "Chapter", "Figure", etc

Advanced options
▪︎Count words until cursor*
▪︎Count words within selection*
▪︎Count footnotes*

Generate word report
▪︎ Analyses your document and provides a detailed breakdown of word count by chapter or subchapter through the use of paragraph styles.

Display modes
▪︎Full
▪︎Minimal
▪︎Barebones Floating

Future
▪︎More features
▪︎Better handling of lone symbols

Tips
▪︎If it does not load, check if you're using multiple accounts, in that case, you can log out of all accounts or use incognito mode. For Chrome users, problems may also arise if you are not using your primary account. Unfortunately, this is a problem on google's side and I can't directly fix it.
▪︎If you're using the addon for long periods, you may want to check the slow update box to ensure that you don't hit the maximum quota.
▪︎For error reporting, try to include console log or any error messages.

Note
▪︎There will not be support for tracking word count over time.

Changelog
▪︎V6.2 Bugfixes (subtitle exclusion)
▪︎V6.1 Bugfixes (core counting method table)
▪︎V6.0 Major update to core counting method and bugfixes
▪︎V5.1 Improved word report interface
▪︎V5.0 Generate word report now shows words that were excluded. Added option to disable exclusion of table of contents. Added option to exclude double-quotes. Added option to make counting algorithm more similar to Google Docs behaviour.
▪︎V4.1 New setup menu for new users
▪︎V4.0 Reading time estimate and input validation
▪︎V3.13 Bugfixes (Footnotes & Logo)
▪︎V3.12 Bugfixes
▪︎V3.11 Count words within selection
▪︎V3.10 Styling improvements
▪︎V3.9 Barebones floating mode
▪︎V3.8 New splash screen 
▪︎V3.7 Stability improvements and bugfixes