I think that's a problem of native English speakers that doesn't affect native Dutch (or German) speakers. It has to do with which vowels and consonants you are used to distinguishing. For native Dutch speakers, the subjective difference between ee and ie isn't as much smaller than that between ee and oo or between ie and oo (Dutch pronunciation in all cases) as it is for native English speakers. English doesn't have these exact sounds, so native English speakers try to make sense of them as English vowels that are similar. For a native English speaker, the sound of Dutch ee is somewhere between the vowels of English pear, pay and peer, and the sound of Dutch ie is almost exactly like that in peer. If you have the problem you describe, it means that your mind automatically classifies Dutch ee as the vowel in peer (just like it does for ie), rather than e.g. the one in pay, as is customary for French words that end in the letter written é and pronounced identically to Dutch ee. (The problem with the pay approximation is that there is definitely no change to an y sound (similar to the vowel in pit) at the end of Dutch ee and French é.)
There are similar issues for the distinction between w and r. The pronunciations of these consonants differ a lot between Dutch and English, so again they need to be reclassified. There is already a minor problem here in German and Dutch under non-optimal circumstances, but for English speakers it's even worse.
Children learn to classify the sounds of their native language in their first year of life. Adding new classifications as an adult is extremely hard. This is probably the main reason for the phenomenon of foreign accents. Some adults adapt to the sound classification of a new language within about a year of complete immersion, and some never adapt even after migrating as a teen and decades of immersion.
It's best to stick to één for one and een for a/an. If you leave out the accents, everybody will read it as a/an by default (since the article is way more common than the number). However there are some situations where there can be no mistake, in those situations the accents are usually left out. For instance eenentwintig or het een en ander (a fixed expression).