What should I do to make it more even?
(sigh)... Well, sadly, a change in the rules is certainly not something you or I can do, and is up to Konami to decide if they want to change that part or not. Perhaps when some time passes and the Link dynamics start to settle in they will adapt the rules a bit to support those decks that do not use Links as part of their deck.
However I must warn you that Konami strongly favors new cards and archetypes they come up with; when Synchro monsters first appeared 'older' decks were strongly affected, and in that moment only people with Synchros were able to play and build competitive decks. Same story when the XYZ monsters came about, as Synchros and other older cards started to lose their Top Tier qualities.
This story repeated itself when Pendulum monsters came out, and I guess this is happening again with the new Link monsters. Of course there are exceptions, but you have to get more creative when trying to cope with the change of the Meta game while still playing with your 'older' cards
Personally, my main deck is Harpie Ladies, and fortunately they have been given some support lately that has enabled me to adapt them to make them more competitive (made them more XYZ focused, included some useful Synchros, and took advantage of Top Tier cards like Number 11: Big Eye or Mecha Phantom Beast Dracossack... my wallet was not so happy though, as Dracossack rounded $150 each on that moment). But even after that, with these new changes my dear Harpies are starting to stay behind once again.
A few cards that means that I have a lesser disadvantage to my play or makes my deck counter those disadvantage
This I think is the option you got, and is what I did with my Harpies to compensate for the fast changes of the format; start including in your 'older' decks cards that can counter Link monsters, instead of just having them on your Side Deck.
There are, of course, many cards that you could include to achieve this. I'll be adding some of them here as they come up to mind, so you can perhaps edit your deck to include them to counter Link monsters more effectively:
The Accumulator: «Gains ATK equal to the combined Link Ratings of all Link Monsters on the field x 300.» This can be useful to easily overcome with higher Atk those decks that extensively use Link Monsters. It's Lvl 1 card so you can normal summon without tribute.
Summon Limit: «Neither player can Summon more than two times per turn. (Negated Summons count toward this limit. Negated cards/effects that would Summon do not count.).» This will help you prevent your opponent from Link summoning right away, as all Link monsters require at least two monsters to summon, so in most cases they will have to wait until their next turn to make a third summon.
Grand Horn of Heaven: «During your opponent's Main Phase, when they would Special Summon a monster(s): Negate the Summon, and if you do, destroy that monster, then your opponent draws 1 card, then end the Main Phase» This and other variants of Horn of Heaven are useful to stop Special summons (like Link summons), halting altogether your opponent's efforts to Link summon. You could also use any of the Solemn Counter Trap cards, which are the most widely used across many decks to stop summonings and other activations.
Kaiser Colosseum: «If there is 1 or more monster(s) on the field of the controller of this card, his/her opponent cannot place a monster on the field if his/her number of monsters would exceed the number of monsters that are on the field of this card's controller. The cards that are already on the field before this card's activation are unaffected by this effect.» If you manage to summon one powerful monster, you can zone out your opponent and make him unable to summon more that one monster (thus no Link). Unfortunately, at the date of this edit this card is forbidden, but may return.
Creature Swap: «Each player chooses 1 monster they control and switches control of those monsters with each other. Those monsters cannot change their battle positions for the rest of this turn.» This is a really powerful card that does not even target and enables you to take control of your opponent's monsters in exchange of one of your own; if they have a single powerful Link monster, you can take control of it by swapping it for any token or lesser monster you have. A similar card is Mind Control but has more restrictions. Even so it can be user to get out of your way some Link monster at least for one turn.
You could also opt for an "Anti-Meta" deck for a change, or well consider some of the cards they use, as those hardly get outdated and still can manage to counter many modern decks (those linked are just a few, you can well make your own anti-meta deck). However, these decks are more control than aggressive or combo, so be sure you like that game play before deciding.
