Yes - backlinks will not add power overnight (so 4 months) is a fair enough measure... assuming as discussed above, that you know that all those backlinks you added hare all been cached / exist and can be seen (are not hidden and that there is no obvious reason that those links might be discounted e.g. due to pages the backlinks are on, being loaded with spam backlink posters).
However, what I would check next, is the competitors who are ranking above you, to see why they are still outranking you?
e.g.
a) how many backlinks they have in google (for the page which is ranking for the targeted keyword)
b) do they have some very powerful backlinks (e.g. from news sites, authority sites etc.)
c) is the over power of their site high (i.e. total number of external and internal links and number of pages cached) e.g. a massive site will outrank a very small one (as the number of backlinks going to many pages, gives them the juice / authority, that the smaller site does not have to more easily rank for keywords).
What well could be happening is that they are building backlinks as fast as you are building them (or getting backlinks at more authoritive sites, so they can rank with less, better backlinks) or even switching anchor text on some backlink surces they control to counteract your attack.
Remember, if you don't watch your competitors, then you can not count them out as the cause (or narrow down, why you are not moving up in the rankings as fast as you would expect).
Sometimes, what you may find is that perhaps you may never be able to beat some of those competitors, with the current level you are adding backlinks for some of the keywords.
I suggest you use seo-spyglass to check this and target the achievable keywords (e.g. if you see someone with 130,000 backlinks to a page or a handful of say very high juice top news site links, think if you realistically have the resources to compete with them or not?).
In regards to checking internal site SEO issues (onpage / site structure issues)... personally I would do that now anyway (web-site audior does a good job of checking site seo issues e.g. checking 404 errors, duplicate pages (titles, descriptions) etc., optimising a page for the keywords you are targeting etc.
I wouldn't wait 4 or 6 months to check onsite issues, as really if your site has major errors (or the page you are pointing backlinks to, is not optimised for those keywords and has though keywords appearing on the page etc.) - you are not going to rank well for them easily, with just backlinks (unless there are no competitors - which sounds like is very unlikely with the keywords you are targeting).
Remember, it is as you know, a team game for seo (onpage and offpage need to be in sync to achieve the results you want) - the easy fix (assuming programming code / closed site code access etc. does not stop you) is fixing the site issues.
If things still seem really strange, then check the outgoing links on your own site (e.g. comments to blog posts), to make sure your site has not been branded by the search engines as a spam source (I have seen this happen to people before and them essentially getting a penalty, due to bad neighbour-hoods sneaking content onto old forum or blog posts they have forgotton about).
I hope you can spot the reason's why some of your competitors are still out-ranking you by using seo-spyglass (and web-auditor, if you think your site might have issues) and get your own site up in the rankings.
Happy SEOing and cheers, Asiaplay
PS: Do send you project to link-assistant support for comments if you can't see why (they are helpful and a good source of neutral assistance / ideas)... tbh this is also a part of why I like this software, as link-assistant do not leave people using their software lost and are willing to help when they can and do ask via support
