You should have used 301 redirects which infer a 'permanent' move from one place to another. Google doesn't send link juice through 301 redirects because that's what the SEO industry says they should do, it's the other way around. Status code 301 infers that the contents of a web page have permanently moved from one URL to another, thus is 'may' be fair to shift all (or a portion) of SEO (ranking) equity from one address to another
Note that even if you do the right thing at the right time, it won't always work. If your redesign heavily removes content (which was previously perceived as useful) from a web page, don't expect the 301 redirect to carry 'all' the link juice from one page to another. Had this recently with a client who decided to streamline some of their more in-depth articles as part of a site redesign and move to HTTP (simultaneously). They did correctly use 301 redirects (A to B, nothing in the middle) and they did point all the posts from the old HTTP URLs to the HTTPS URLs on the new site (same domain, but again - protocol altered and change of design)
Because the posts contained quite radically different (stripped down) content on the new site, the 301 redirects only seemed to pass across between 25% and 33% of the ranking equity. They did everything right, but if you're telling Google that content has moved from one URL to another, you had better actually move the content (lies don't work)
If you take into account that, even doing most things correctly you can cause some major issues, if you use the wrong response code then obviously you greatly increase the risk of losing all (or much of) your ranking power
I'm going to say this now, one year is probably way too late to get back to where you were just by changing some redirects. If that's your expectation, check yourself before you wreck yourself. Redirects (of any kind) slowly decay over time and most people think that a lot of the equity transfer has occurred by six months, let alone twelve. If you transferred your ranking equity into the void of cyberspace... well, it's probably 'mostly' gone by now. I'd still recommend converting the redirects as it really is your only option other than building your ranking equity over from scratch
**Let's get onto, why what you did was wrong **(why is important!)
So to you, a '303' is a type of redirect. But in its wider context, it's actually a 'status code'. Not all status codes result in a redirect and they all mean completely different things. They basically tell a client or a web-browser, which makes a request (that results in some kind of error), what the best way to proceed is. Some just send information back, others perform more concrete actions like the 3XX codes (redirect codes)
One common thing we get on here is, people saying: "I want to de-index some pages from Google, but I can't get Meta no-index into the source code, what can I do?" - very often I look at those questions and find, the pages which they want de-indexed are sending status code 404. Status code (error) 404 simply means "this resource or page isn't available temporarily, but keep tabs on it because it's only temporary and it will be back". So quite often I suggest to them, well you can deploy no-index in the HTTP header via X-robots, but also why don't you change the status code from 404 to 410? Status code 410 roughly means "gone, not coming back so don't bother coming back"
You did use a redirect code, but you used the wrong one which had the wrong meaning:
So what does status code 303 mean?
I cite from Wikipedia:
"The HTTP response status code 303 See Other is a way to redirect web applications to a new URI, particularly after a HTTP POST has been performed, since RFC 2616 (HTTP 1.1).
According to RFC 7231, which obsoletes RFC 2616, "A 303 response to a GET request indicates that the origin server does not have a representation of the target resource that can be transferred by the server over HTTP. However, the Location field value refers to a resource that is descriptive of the target resource, such that making a retrieval request on that other resource might result in a representation that is useful to recipients without implying that it represents the original target resource."
So in English a 303 translates roughly to:
"Hey web user. I can't give you the page you are requesting because it's gone, and I can't redirect you to that same content on another URL because guess what? It wasn't moved to another URL. That being said, I think this page I am going to send you to, is at least partially relevant. I'll send you there - ok?"
But you're only stating that the resource is partially equivalent, so you can only expect fractional (at best) equity transfer from one URL to the other
Using a 301 tells Google: "this exact page has moved to this other exact page and it's likely to be 75% the same or higher overall. Ok so maybe we changed how the nav menu looks an moved to HTTPS, but the written content and images and stuff that was unique to this page to begin with - that should basically be all the same. As such, you don't need to re-evaluate the ranking potential of this page"
... of course, Google still will (in many instances) re-evaluate the page against the query, which is why (although loads of people say they do) - 301 redirects don't always transfer 100% of your SEO equity. If the content is adjusted too much, even 301s don't save you and it's time to build up again from ground zero
As stated redirects decay over time as the SEO equity moves from one place to another. In your case you have asked Google to move one portion of the equity from one URL to another (which they may or may not have, depending on content alterations) and also to delete the remaining portion of your ranking power. If that movement is now complete, then gains from fixing the redirects won't be all you are hoping and dreaming of
It will help. Be sure that you do it, because it's a seconds to minutes change in your .htaccess file or web.config file. It's not hard, it's very simple and you could luck out. But with a whole year behind you... the odds aren't fantastic. Still it's some 'free' equity that you can get back, which you won't have to re-earn (so take it). But it won't be all-encompassing (sorry)