I don't about humble. At one Masters tournament he said of another golfer (might have been Arnie), "How the Hell did that guy ever get invited to the Masters?!" It might have been at that same Masters, or maybe at the 1960 US Open at Cherry Hills, he was paired with Jack Nicklaus the first two rounds. After the second round he was talking to the press and said, "I played two rounds with some fat kid who, if he understood anything at all about the game, would have made this place look silly!"
Since you originally mentioned that you were going to go to a Fitter for this next set of irons I would suggest that you go into it with a complete and open mind.
Trust your Fitter and the equipment he/she is using. Launch monitors do not lie, they present cold hard facts as to what is and is not working. Hopefully your Fitter is using a Trackman but if not I would not consider that a deal breaker.
You might very well be surprised that what you visually prefer to look down at will also perform the best for you or near the very top of the list of clubs.
This then speaks to the general statements that are made that this, particular type of handicap works best with this type of club. Throw those general statements out the window and stick to an open mind about what is going on with your fitting session. The reason for that is you are a specific situation, not general. What may work for a general group of players may very well not work for you.
Just because you are a "Mid Handicap" player does not mean the GI or SGI irons are the best fit for you.
I know this as a fact for me. When I went into my last iron fitting I was running between a 12 & 16 handicap. I told my Fitter that I should look at GI & SGI irons. Shortly into the fitting he took both of those categories out and focused on Blades and Player's Irons. My Fitter told me that I hit smaller club faces consistently center while hitting the GI and SGI irons I was all over the face.
My Fitter told me it was pretty much a toss up between Blades and Players Irons but he wanted me to buy Players Irons because they had enough forgiveness in them to help me.
After purchasing my current irons my handicap did drop. The correct irons helped but I also really like hitting them thus I really enjoy going to the range and practicing with them, which all lead to dropping my handicap.
As to your last question, yes there are a lot of choices with little to no offset while also having a thinner to mid top line. Mizuno, Ping, Titleist are some that come to mind.
if you can't reach the par 4's in 2 shots, then, i dunno what to tell you, other than youre playing the wrong tees lol. golf is hard man, eagles are tough, and hole in ones are near impossible believe it or not there are pga tour players who get a hole in one in a tour event and it's literally their first hole in one EVER, meanwhile some low handicappers have multiple hole in ones in their lifetime. I have 0, but I'll take near par rounds over a hole in one while shooting 80 any day. I only just this year got my first eagle after driving a 260 yard par 4 and draining a 15 foot putt. I've started to come close on some par 5's this year too as I'm now starting to hit the green on 2nd shots, but again, my focus is not on getting the eagle but rather setting up easy birdies and making pars as my 2019 goal was to break 80, which I now do regularly, so my next goal is to shoot par on a full 70/72 course.
as far as advice goes, you probably just have to be better. eagles start with a good drive and a solid 2nd shot. Know your distances, and be a solid ball striker so your shots actually go those distances 80% of the time, not just once in a blue moon. I mean, unless youre getting 3-4 birds a round, what makes you think you deserve to get eagles?
Interesting. Sometimes at the range I'll play a "simulated" round. I pick a local course I know well and imagine I'm there. First hole, 399yd par 4, hit Driver from the tee. I pick a particular target that represents the fairway. How far I hit it determines the club I pull for my approach, and I pick a different target to aim at so I'm not hitting on the same line every shot. And so on.
On the green do some specific drills, like Michelson's circle drill. Also, use a couple of tees to make yourself a "gate" that is about an inch wider than your putter. Put a ball between the tees and stroke some putts. This will train you to strike the ball in the center of the putter face. Heel and toe strikes will mess with you.
In addition to sharpening your short game, if lag putting is a problem then yes, you'll have to work on it. There's a thread on the "Swing Thoughts" page, I believe, titled "Do NOT accelerate when putting", or something to that effect. I've worked on this since I read it and it has improved my putting, especially my lag putting, a lot!
Sometimes, just work on putts from 3' to 5'. If you make a bad lag, and you will, we all do, those are the ones you have to make to avoid 3 putting. And, if you stick your approach close, those are the ones you want to 1 putt. I've heard more than one pro say that it's important to see the ball go in the hole! Over and over again. Practice success!