Hi there, glad to see you’ve found your first foray into monolingual dictionaries to be going quite smoothly, happy to have played a part in your decision 
. My apologies for the late response.
I do have to admit that the Kanji dictionaries are my personal least used dictionaries, and I mostly turn to those only after I already read some entries in an actual dictionary, so already have the word ready, and just need to switch dictionaries. (Bonus tip : You can easily switch between the same entry in different dictionaries by simply clicking the drop-down arrow next to the word (see images))
iPhone :
Desktop :
But I’ll see if I can give you any useful tips on how to use it effectively. The first “tip” I would give you is to consider switching to looking up kanji by stroke count and radicals (if you aren’t in a situation where you can just copy paste), as I feel that this is generally a faster, and - at least to me - way less frustrating way of looking things up. I’ll be using images for the desktop version of the dictionary, but the principle is the same for the iOs version.
How to search by stroke count
With the Shinjigen open, first you need to head to the index, for that, just click on the index button in the top right, a page like this one will appear :
Next, you need to navigate to the stroke count page, namely 総画 (the stroke-count of a kanji), the fourth option down on the right-hand side. This brings you to the following page :
Just click on the number of strokes in the Kanji, and this screen will appear :
Now, on the bottom (or on the right side of the columns) you can see a scroll wheel of radicals. In general I find the most annoying Kanji to be those where the kanji equals the radical, but you get used to and faster with this kind of lookup as you practice. (Addendum : Good article on the official radicals by Our overlords Tofugu )
Now, I totally understand if you don’t like / want to use this type of lookup. It can be quite bothersome, and especially in the beginning it will be slower than drawing the kanji out, but it’s quite a wortwhile exercise in my mind and will also enable you to use an actual physical dictionary for kanji lookup if you ever find yourself in such a situation (plus, it’s great bragging rights if you ask me 
)
Starting from radicals
This is the way to look up that I personally pretty much never use (only on a rare curious foray to see what kind of kanji use a certain radical), but it’s also in general not a bad way to look up Kanji. The difference is simply that here you start with the radical (and the number of strokes in said radical), and then you get a list of kanji with that radical + x number of additional strokes. For this, you first go back to the index and then click on the 部首 on the right. The first page that shows up is this one :
On the bottom and on the right side you see the sorting by the number of strokes. It’s important to note that this is the number of strokes in the radical as opposed to the number of strokes in the kanji that we used in the previous lookup method. From here you can click on the radical in question, and a page like this one will show up :
On the right you see the 部首解説, followed by a list of kanji using the radical + the number of additional strokes past the radical. It’s quite a nifty way to look at all manner of kanji that use the radical. One thing I should note here though, because I use the 肉 radical for my explanation, you might be confused why you are seeing so many entries that seemingly use the 月 radical. This quick wiktionary entry should help clear up any confusion on that front (and also be an excellent showcase on why radical lookups can still be a confusing mess on some occasions, though you do learn the common pitfalls after a while )
Besides these tips, the only thing I can really recommend is to keep plugging away at it and using the dictionary. It really is a skill in and on itself and you WILL get better and faster at it eventually, I promise 
My apologies that I don’t have any better / more useful tips, btw 