I fully agree that RDM needs some way to encourage swapping between casting and melee, and this idea is as promising as any. So, here's my critique, in no particular order.

Just to start, if you really want the job to alternate between melee and magic you should probably re-think the combo bonuses. According to your chart there's no reason to switch, as you can go Sage's Glyph > Dia > Stonera > Blizzara > Fira > Fira II without any melee attacks in between, and vice versa. To continue, you just spam Dia to get back glyph stacks and then combo again from there because nothing you do on the melee side is going to give you more glyphs.

Since Dia is the go-to spell for Glyphs, you might consider switching the DoT to one of the other spells and just making Dia a straight damage spell.

Since you're not using it for tiering, the -ra convention throws the naming off. I'd suggest just throwing the suffix out entirely and using entirely alternate spell names: Burn, Ice, Bolt, Rock, Gale, Spray (you may as well have a water spell too, since it's the only element you left out) and Heal (oh yeah, you don't actually have Cura on the list either), as examples.

TP/MP can probably be ignored with the Glyph/Insignia system in place, although the Glyphs/Insignias are kind of unwieldy, so keeping TP/MP and dropping the buffs might work better. Either way, having both is just extra cost for no real reason other than to have an extra cost. Just give spells combo bonuses from melee attacks and give melee attacks combo bonuses from spells. As a cooldown, Circumvent is still fine making the costs free for 15s. Chainspell would need re-thinking, though, but not for the reason you'd think.

From Chainspell's description, I can see it being saved for use exclusively with Circumvent, meaning, without any changes to the current design, you get 15 seconds of free-cost spells with full combo bonuses and only a 1s cast time preventing unlimited macro spamming. At the current 7 minute recast, it would still give long fights categorically to RDM, as you're getting a possible 15 spells in 15 seconds. If BLM had the same ability, they'd only get 6-7 spells in 15 seconds, depending on Swiftcast. Changing Chainspell to make all spells instant-cast without affecting the GCD, however, would give it good non-game-breaking utility and the recast can be brought down to much more reasonable levels.

You should never have an ability with a Stun you don't directly control attached to it. With no other elemental spikes, Shock Spikes is fine without the Stun, and you should really allow it to be cast on others (like tanks) or else it will just be a solo-only spell.

Likewise, you should never have a Cooldown ability with any cost. Circumvent should be free, and the recast should be dropped to 120s at most.

Chainspell's recast should be 60-90s if it changes to cast time, 180s if you go with a more powerful effect; otherwise even 7 minutes might not be long enough to balance it as it currently is.

Shock Spikes and Flat Blade recasts should be cut in half. Actually, Shock Spikes may as well be a buff spell on the GCD, as the effect is pretty much the same as a weak DoT.

Silence is always used as a reaction with a 1s duration. A 4s duration is just overkill. 30s recast is probably far too long for an ability that does nothing except Silence. Silence isn't necessarily the party-getter it used to be either. A spell like Dispel would have much greater applications, if that's what you were going for.

The affinity column may as well be tossed, since there are no cross-class skills in the list. Saboteur may as well be absorbed into RDM, since the new direction of jobs is to no longer have classes. The current classes may very well be the last classes we ever get.

Melee range for swords (PLD) is 3y.

There isn't much reason to separate the two buffs. Actually, there isn't much reason to have the buffs in the first place since their recast is shorter than their duration, and most combo timers are already at 10 seconds. You could just use combo bonuses to add the glyphs and insignias.

You should also have a weaponskill (Swift Blade) or spell (Dia), or even Shock Spikes just to be different, at 1st level, as the buffs do nothing for a 1st level character.