Having been riding for 3 years makes a difference, doesn't matter what kind of bike. Regular rides of 40k is not bad in the context of a 60k race, but others have probably been riding far more for this distance race. Riding 60k and racing 60k are very different unless you don't mind being the lantern rouge, the last rider to finish. Increasing mileage is best done in steps. If you are comfortable riding 80-90k 2 months out or 1 month out won't imo make a big difference.
Riding shorter distances at faster speed is a good way to increase average speed, the interval. It's best to do intervals once you have a level of basic fitness, however they will improve fitness regardless. Don't worry about the speed in kph you reach during the interval, it's really about level of effort. Imagine someone much fitter, both of you would do the same interval at different speeds.
There are many different types of intervals but to reduce these to two basic types makes things easier. There are many variations.
To keep it simple let's just call them the long interval (the threshold interval) and the short (VO2 max) interval. Even with these the length of time and intensity could vary but again we'll just keep it simple for now. Personally I keep a pretty similar cadence whatever the intensity I am riding at (90-105), but when climbing the cadence drops a bit. These are my personal preferences, others do it differently, this is one of the things that takes time, learning what is best for you.
Ok, the long interval: anywhere from 10-20 minutes. I usually start at around 10-12 minutes, and around 80-85% of my MaxHR, faster than tempo, but slightly slower than my time trial pace. I increase the length of time as the season progresses. After a good level of fitness achieved by just riding for a couple months I'll add these. 2x10 minutes in the first couple weeks, then 3x10 the next couple weeks, 3x15, 2x20, etc. slowly increasing the time of the interval, not the intensity.This is not a rule, others do it different, ramp it up different, that's them. Twice a week on these workouts for me. These intervals help to increase your cruising speed. If you don't have an HR monitor, it would be approximately 7 on a scale of 1-10 imo. Only short sentences possible or maybe faster. Once fit, you could do these year round. My rule of thumb for rest between: .5 to 1 So for a twenty minute interval I am resting 10 minutes between each. I often do these as hard as I can go or close to it for that time-frame (which I guess is technically my TT pace).
The short interval: my personal favorite is between 2-3 minutes. These are tough. 89-92% of MaxHR. 9 on a scale of 1-10, pretty much all out but not a sprint. I do these starting 4-5 weeks before the opening season race, some like to start 6 weeks out, or more. Week 1 would be something like 3x2mins, or 3x3mins. I would not do this workout more than twice a week. Each week I would add a repetition. So by the 4th week it would be 5x2mins. Some people break these into sets with a bigger rest between. i.e. 2[3x3min]. Rule of thumb for rest is 1 to 1. So for a 2 min interval, 2 mins of rest between reps, a 3 minute, 3 mins of rest between each (a 2:1 rest between multiple sets. i.e 6 minutes for a 3min interval set). Some like more rest, some like less rest. But too much rest between and your body won't adapt as quickly to processing lactate. Because heart rate lags, it is easy to start these too hard. Some like to start explosively (at max effort), I like to build up to max over 20 seconds or so. If you cannot complete your set, you went out too hard. If you are not pretty tired after you finish, you went to easy. In my opinion the real value of this exercise, aside from being able to increase your bodies capacity to process lactic acid, is learning how your body works at red line, right on the edge of your own abilities, without going over, also known as "blowing up". Some like to do them a little longer, an intensity maintainable for 5 minutes or so, which would target many of the same energy systems. The 2-3 minute variety both improve capacity to carry oxygen as well as process lactate, like killing two birds with one stone. If I were doing the long version of the "VO2" interval (5 or 6 minutes) then I would also be doing shorter, harder, 1 minute efforts with more reps (up to 10) to focus solely on the ability to process lactate. i.e. breaking the short version into 2 further categories. These workouts are both very mentally as well as physically demanding because of the difficulty.
Because the short interval significantly increase the overall workload it is good to bring down the length of your long distance rides a little as you increase the intensity of your workouts. And getting ready to race I would stop doing any real intensity at least a week or so out so you are fresh for your race.
The better your aerobic base, the easier it is to recover from these workouts. Think of your fitness as a pyramid with the aerobic stuff (65-80% of maxHR) making up the base, with the short intervals at the tip of the pyramid. It's a very stable structure. Try to turn the pyramid upside down (intervals without a solid level of basic fitness) and it will easily topple over. It's what I like to refer to as "fragile" top-end fitness. Stronger and faster, but fitness gains (which can be quite substantial if out of shape) will be short lived and dissipate quickly. When seasoned athletes get sick and are off the bike this is the stuff that disappears first, the base remaining largely intact.
I have written only a few paragraphs, there are entire books dedicated to this. This is a simplified approach.
I would still put more focus on slowly increasing the mileage so you able to ride more than the race distance quite easily. Then worry about the speed work. 4 months is certainly enough time.
... a labor intensive answer. [Edit: But with no objection. It'll will be helpful to find others to ride with and learn how to ride comfortably in someone's draft. One of the big diffs between road and mountain is conserving energy this way. Not too close because when wheels overlap the guy in the back usually goes down, and not to far because then there's no benefit. Solo speeds are not indicative of race speeds which are usually quite a bit higher because of the aerodynamic gestalt of the peleton. But for an entry level category race 30+kph solo cruising speed would be better, large group speeds can quickly exceed 40kph and by quite a bit when it's hammer time. Don't be discouraged if you can only do 30kph+ for a short time, when Michael Hutchinson attempted the hour record, a few months out he could only maintain the speed he needed to beat the record for a few minutes, not even close to sixty minutes! He didn't ultimately beat it, but he came pretty close. There's some other edits too.]