I would like to thank everyone who offered a solution or an opinion under this thread that I started 2 weeks ago.
Instead of replying back promptly, I wanted to wait until after trying some of the suggestions and implementing my own experiments. Finding and using sporadic free time took two weeks but I finally completed my trials today. The result is a surprising but a happy story. I will share it because there may be other novice users of baitcasters who one day stumble upon this thread and may solve their problems too.
Having said that I would like to emphasize that it is only my fifth day in the trials and tribulations of baitcasting reels. I am in no position to give advice or claim holding the truth. I am just telling my experience and what worked for me.
Just to recap, I was trying to cast 3/8 oz lure over 40 yards consistently so that I can fish a local lake from the bank. I put a 30lb braided line on the spool and casted a practice plug repetitively on the grass over 40 yards. However, when I took the same set up to the lake with a swimbait, I was getting frequent backlashes when I try to go over 20-25 yards. I suspected that the wet braid was somehow the culprit.
First thing I tried was to change the spool to 15lb mono. I took the same practice plug to the park and I hated every minute of it. It is already known that mono line has memory problems, but I did not know it was this bad on a baitcaster. That line does not want to stay on that reel. Yes, when I cranked the tensioner and the brakes up, I could easily cast 20-25 yards, but reaching to the 40 yards was a problem for me. Resolving minor overruns was as annoying as the backlashes. When using braid, something I can resolve by releasing a foot or two of the line became yards of line release in mono. The spool does not tidy up easily on mono. When there is slack line, I grab the rod in front of the reel and use my thumb and index finger to feed a somewhat tight line to the guide so that the spool is packed tight enough. Yet, when I try to brake with my thumb to slow an overarching cast I always find the spool is couple of turns loose at the end. That rarely happened with the braid, And, when it happened I could resolve it by just pulling a feet of line. So, my experience with mono was so bad that I did not take it to the lake. I am glad that I was lucky enough not to start using a baitcaster reel with a mono line. Otherwise, I would have given up the first day. Life is too short to train for a hobby if one is not enjoying the process.
Then, an idea occurred to me. I know the material of the braided line (ultra-high molecular weight polyethylene) is hydrophobic. If I use a same diameter but 8-strand braided line instead of 4-strand, I can reduce the surface area and make the line even more hydrophobic. Also, I do not know how tightly the 4-strands weaved together, but when I hold my 30lb 4-strand braid I can feel the roughness. That is another indication that surface may have a lot of micro-pools/crevices that can hold water. So, I decided to get a 30lb, 8-strand line.
On the 4th day of trials, I went to the park with the same practice plug but a 8-strand 30lb line. It was beautiful again. I was consistently casting above 40 yards. (My line was unicolor so I was counting my strides.) I stayed around 90 minutes at the park, maybe casted 40 times. I had a single backlash and it was an obvious aiming error.
So, on day 5, today, I went to the same lake again, put the same lure on and started casting. It was enjoyable. I could not measure the distance, but I am guessing high 30s if not 40. After the first hour I switched to 1/2oz. Johnson minnow spoon. It was flying. I was so happy. I stayed 4 hours at the lake. In the first 3 hours, I probably got 10 backlashes, but they were nothing I could not resolve under a minute. Half of them were due to unrelaxed casting in the presence of branches. And in between those backlashes, it was very enjoyable. This is something I can built on.
About the braided line: not just my casting improvement, but also the sound the line makes during the casting attest to the fact that 8-strand holds less water. When I was casting with the 4-strand line on the water, it was making this annoying, almost screeching, sound during the cast. That sound is gone with the 8-strand. Also, when I thumb the spool with the 8-strand after a wet cast, it feels damped but nowhere as drenched as the 4-strand.
In the last hour, close to noon, the wind started to pick up. I used that as an opportunity to practice with the wind. I first casted couple times directly towards it. Unsurprisingly, all backlashed. But with a lot of brake (6/10) and tensioner, I can cast direct to the 10-knot wind 15-20 yards. That was surprising. What is more educational, and fun was to cast perpendicular or nearly perpendicular (>70 degrees) to the wind. One can observe and experiment how sensitive the reel is to the speed of the spoon. My thumb is not trained enough and that becomes more apparent during the wind. When I increase the cast arch more than 5 degrees, I cannot compensate it with my thumb, I needed to increase the brakes one notch (4/10).
Anyway, it was a fun day, I wished I caught a trout (it is a trout lake) and posted a picture here to do a Hollywood ending but could not catch any. On three different casts they chased the lures all the way to bank but no bite. I guess the inflation affected the trout as well. They were just window shopping.
Thank you all.