I genuinely enjoy working at the company and do not want to unintentionally sour the relationship with the leadership.
You need to consider your perspective on this carefully.
You've worked 18 months without a pay rise, when 12 months is typically the outer limit for at least a normal inflation pay rise, unless the market for your work has changed radically for the worse.
That is notwithstanding the salary increase that should be attributable to increased experience and overall career progression, unless your career is already over the hill.
Also, why should managers be angry that you're asking for the market rate of pay, which they are currently offering to new hires? If they are angry at the mere mention, then typically the best response is to seek market pay elsewhere.
The starting point in any negotiation should be that you're entitled to at least an inflation pay rise, without any special justification. An inflation pay rise means your employer is simply paying you the same as before, relative to the general level of wages and prices in the economy.
Next, if market demand for your occupation has surged since your pay was last set, then you'll want to go armed with information about the level of market wages for your occupation generally. You do not need to justify this by any exceptional performance in your current position - the market level is what another employer will pay for an average candidate hired fresh.
Finally, if you have performed exceptionally well in your current role, you will want to go armed with details about your achievements so as to justify why you should be paid at the higher end of the general market range.
Should I bring this up to my manager now or wait until promotion opportunity (supposedly happening soon) and attempt to renegotiate?
Unless the opportunity is already on the calendar and imminent in the next month or so, then I would start discussing the pay rise now.
Your employer obviously has no particular rhythm, otherwise they would not have gone 18 months already. If you are rebuffed, then be insistent that you want to talk about pay now.
If you delay, your manager might well attempt to "promote" you but then give you only the rise you could have achieved at your current level. You might even be denied a raise completely, as sometimes employers try to suggest the promotion itself should be seen as a favour.
If you don't get the right response, then seek better pay at a new employer. This will act as a double sting for your current employer - they will not only have to recruit someone on the market pay they could have satisfied you with, but will have to pay that same level to a new hire (who could turn out to be of a different calibre) and with the loss of your accumulated experience.